Subgroups — C₄₃×#10729 #24930746

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#344	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₃	—	2	2	no	—
7	C₂²×M₁₆×C₄₃	—	2	2	no	—
8	C₂²×M₁₆×C₄₃	—	2	8	no	—
9	C₂²×M₁₆×C₄₃	C₄	1	2	yes	complemented
10	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
12	C₂³×C₈×C₄₃	C₄	1	2	yes	complemented
13	C₂×#117×C₄₃	C₂²	1	2	yes	—
14	C₄₃×#407	—	2	2	no	—
15	C₄₃×#407	C₄	1	2	yes	complemented
16	C₄₃×#407	C₄	1	2	yes	complemented
17	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
18	C₄₃×#381	C₄	1	2	yes	—
19	C₄₃×#380	—	2	2	no	—
20	C₄₃×#379	C₄	1	2	yes	—
21	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
22	C₄₃×#344	—	2	8	no	—
23	C₂⁵×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₃	—	2	4	no	—
25	C₂³×C₄×C₄₃	—	2	4	no	—
26	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₃	D₄	1	2	yes	—
32	C₂³×C₄×C₄₃	D₄	1	2	yes	—
33	C₂³×C₄×C₄₃	D₄	1	2	yes	—
34	C₂³×C₄×C₄₃	Q₈	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₃	—	2	16	no	—
37	C₂×M₁₆×C₄₃	—	2	16	no	—
38	C₂×M₁₆×C₄₃	—	2	4	no	—
39	C₂×M₁₆×C₄₃	—	2	4	no	—
40	C₂×M₁₆×C₄₃	—	2	2	no	—
41	C₂×M₁₆×C₄₃	—	2	2	no	—
42	C₂×M₁₆×C₄₃	—	2	2	no	—
43	C₂×M₁₆×C₄₃	—	2	8	no	—
44	C₂×M₁₆×C₄₃	—	2	4	no	—
45	C₂×M₁₆×C₄₃	—	2	4	no	—
46	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₄₃	D₄	1	8	yes	—
48	C₂²×C₈×C₄₃	—	2	4	no	—
49	C₂²×C₈×C₄₃	—	2	8	no	—
50	C₂²×C₈×C₄₃	—	2	2	no	—
51	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
52	#117×C₄₃	—	2	4	no	—
53	#117×C₄₃	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₄₃	—	2	2	no	—
58	C₂²⋊C₈×C₄₃	—	2	4	no	—
59	C₂²⋊C₈×C₄₃	—	2	4	no	—
60	#95×C₄₃	—	2	4	no	—
61	C₂⁴×C₄₃	—	2	4	no	—
62	C₂⁴×C₄₃	—	4	4	no	—
63	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
64	C₂⁴×C₄₃	C₄²	1	1	yes	characteristic
65	C₂⁴×C₄₃	C₂²⋊C₄	1	2	yes	—
66	C₂⁴×C₄₃	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	4	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	8	no	—
77	C₂²×C₄×C₄₃	—	2	8	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	4	no	—
82	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	4	yes	—
102	M₁₆×C₄₃	—	2	16	no	—
103	M₁₆×C₄₃	—	2	8	no	—
104	M₁₆×C₄₃	—	2	8	no	—
105	M₁₆×C₄₃	—	2	8	no	—
106	M₁₆×C₄₃	—	4	4	no	—
107	C₂×C₈×C₄₃	—	2	16	no	—
108	C₂×C₈×C₄₃	—	2	4	no	—
109	C₂×C₈×C₄₃	—	2	4	no	—
110	C₂×C₈×C₄₃	—	2	4	no	—
111	C₂×C₈×C₄₃	—	4	2	no	—
112	C₂×C₈×C₄₃	—	4	2	no	—
113	C₂×C₈×C₄₃	C₂²⋊C₄	1	8	yes	complemented
114	C₄⋊C₄×C₄₃	—	4	4	no	—
115	C₂²⋊C₄×C₄₃	—	2	8	no	—
116	C₂²⋊C₄×C₄₃	—	4	8	no	—
117	C₄²×C₄₃	—	4	2	no	—
118	C₄²×C₄₃	—	4	2	no	—
119	C₂³×C₄₃	—	2	4	no	—
120	C₂³×C₄₃	—	2	2	no	—
121	C₂³×C₄₃	—	2	4	no	—
122	C₂³×C₄₃	—	2	4	no	—
123	C₂³×C₄₃	—	2	2	no	—
124	C₂³×C₄₃	—	2	4	no	—
125	C₂³×C₄₃	—	2	4	no	—
126	C₂³×C₄₃	—	4	2	no	—
127	C₂³×C₄₃	—	4	2	no	—
128	C₂³×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	4	2	no	—
130	C₂³×C₄₃	—	4	16	no	—
131	C₂³×C₄₃	#95	1	2	yes	—
132	C₂³×C₄₃	#95	1	2	yes	—
133	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
134	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₄₃	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₄₃	—	2	2	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	4	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	4	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	2	4	no	—
149	C₂×C₄×C₄₃	—	2	4	no	—
150	C₂×C₄×C₄₃	—	2	4	no	—
151	C₂×C₄×C₄₃	—	4	8	no	—
152	C₂×C₄×C₄₃	—	4	4	no	—
153	C₂×C₄×C₄₃	#95	1	2	yes	—
154	C₂×C₄×C₄₃	#95	1	2	yes	—
155	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#117	1	2	yes	—
161	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
162	C₂×C₄×C₄₃	#120	1	2	yes	—
163	C₂×C₄×C₄₃	#120	1	2	yes	—
164	C₂×C₄×C₄₃	#121	1	4	yes	—
165	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
166	C₂×C₄×C₄₃	#123	1	2	yes	—
167	C₂×C₄×C₄₃	#123	1	2	yes	—
168	C₈×C₄₃	—	2	8	no	—
169	C₈×C₄₃	—	4	4	no	—
170	#10729	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₄₃	—	2	8	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	—	2	2	no	—
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	2	2	no	—
180	C₂²×C₄₃	—	4	4	no	—
181	C₂²×C₄₃	—	4	8	no	—
182	C₂²×C₄₃	—	4	8	no	—
183	C₂²×C₄₃	—	4	4	no	—
184	C₂²×C₄₃	#344	1	4	yes	complemented
185	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
186	C₂²×C₄₃	C₄×C₂²⋊C₄	1	2	yes	—
187	C₂²×C₄₃	#385	1	2	yes	—
188	C₂²×C₄₃	#386	1	2	yes	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	8	4	no	—
192	C₄×C₄₃	#379	1	1	yes	characteristic
193	C₄×C₄₃	#380	1	2	yes	—
194	C₄×C₄₃	#381	1	1	yes	characteristic
195	C₄×C₄₃	#385	1	2	yes	—
196	C₄×C₄₃	#386	1	2	yes	—
197	C₂³×M₁₆	C₂×C₄₃	1	1	yes	characteristic
198	C₂×#407	C₂×C₄₃	1	1	yes	characteristic
199	#2280	C₂×C₄₃	1	1	yes	characteristic
200	C₂×#344	C₂×C₄₃	1	4	yes	complemented
201	C₂×C₄₃	—	2	2	no	—
202	C₂×C₄₃	—	2	4	no	—
203	C₂×C₄₃	—	2	2	no	—
204	C₂×C₄₃	—	2	2	no	—
205	C₂×C₄₃	—	4	2	no	—
206	C₂×C₄₃	C₂²⋊#95	1	1	yes	characteristic
207	C₂×C₄₃	C₂×#344	1	2	yes	—
208	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
209	C₂²×M₁₆	—	2	2	no	—
210	C₂²×M₁₆	—	2	2	no	—
211	C₂²×M₁₆	—	2	8	no	—
212	C₂²×M₁₆	C₄×C₄₃	1	2	yes	complemented
213	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
215	C₂³×C₈	C₄×C₄₃	1	2	yes	complemented
216	C₂×#117	C₂²×C₄₃	1	2	yes	—
217	#407	—	2	2	no	—
218	#407	C₄×C₄₃	1	2	yes	complemented
219	#407	C₄×C₄₃	1	2	yes	complemented
220	C₂×C₂²⋊C₈	—	2	2	no	—
221	#381	C₄×C₄₃	1	2	yes	—
222	#380	—	2	2	no	—
223	#379	C₄×C₄₃	1	2	yes	—
224	C₄×C₂²⋊C₄	—	2	2	no	—
225	#344	—	2	8	no	—
226	C₄₃	#10729	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁵	C₂×C₄×C₄₃	1	1	yes	characteristic
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	—	2	4	no	—
230	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
231	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
234	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₄₃	1	2	yes	—
236	C₂³×C₄	D₄×C₄₃	1	2	yes	—
237	C₂³×C₄	D₄×C₄₃	1	2	yes	—
238	C₂³×C₄	Q₈×C₄₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
240	C₂×M₁₆	—	2	16	no	—
241	C₂×M₁₆	—	2	16	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	8	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	—
251	C₂×M₁₆	D₄×C₄₃	1	8	yes	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	8	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	C₂×C₄×C₄₃	1	4	yes	—
256	#117	—	2	4	no	—
257	#117	—	2	4	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	#95	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	4	4	no	—
267	C₂⁴	C₄²×C₄₃	1	1	yes	characteristic
268	C₂⁴	C₄²×C₄₃	1	1	yes	characteristic
269	C₂⁴	C₂²⋊C₄×C₄₃	1	2	yes	—
270	C₂⁴	C₄⋊C₄×C₄₃	1	2	yes	—
271	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	C₄²×C₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₄²×C₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
289	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
290	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
291	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
292	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
293	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
294	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
295	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
296	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
297	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
305	C₂²×C₄	#41×C₄₃	1	4	yes	—
306	M₁₆	—	2	16	no	—
307	M₁₆	—	2	8	no	—
308	M₁₆	—	2	8	no	—
309	M₁₆	—	2	8	no	—
310	M₁₆	—	4	4	no	—
311	C₂×C₈	—	2	16	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	C₂²⋊C₄×C₄₃	1	8	yes	complemented
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	4	8	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	16	no	—
335	C₂³	#95×C₄₃	1	2	yes	—
336	C₂³	#95×C₄₃	1	2	yes	—
337	C₂³	C₂×C₄²×C₄₃	1	1	yes	characteristic
338	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
339	C₂³	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
340	C₂³	C₄×D₄×C₄₃	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	#95×C₄₃	1	2	yes	—
358	C₂×C₄	#95×C₄₃	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
364	C₂×C₄	#117×C₄₃	1	2	yes	—
365	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
366	C₂×C₄	#120×C₄₃	1	2	yes	—
367	C₂×C₄	#120×C₄₃	1	2	yes	—
368	C₂×C₄	#121×C₄₃	1	4	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
370	C₂×C₄	#123×C₄₃	1	2	yes	—
371	C₂×C₄	#123×C₄₃	1	2	yes	—
372	C₈	—	2	8	no	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	C₄₃×#344	1	4	yes	complemented
388	C₂²	C₂×#95×C₄₃	1	1	yes	characteristic
389	C₂²	C₄×C₂²⋊C₄×C₄₃	1	2	yes	—
390	C₂²	C₄₃×#385	1	2	yes	—
391	C₂²	C₄₃×#386	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	8	4	no	—
395	C₄	C₄₃×#379	1	1	yes	characteristic
396	C₄	C₄₃×#380	1	2	yes	—
397	C₄	C₄₃×#381	1	1	yes	characteristic
398	C₄	C₄₃×#385	1	2	yes	—
399	C₄	C₄₃×#386	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	2	2	no	—
403	C₂	—	2	2	no	—
404	C₂	—	4	2	no	—
405	C₂	C₄₃×C₂²⋊#95	1	1	yes	characteristic
406	C₂	C₂×C₄₃×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
socle	C₂²×C₄₃	C₂×#95
prime radical	C₂⁵×C₄₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₃×#344	C₂	semidirect
9. C₂²×M₁₆×C₄₃	C₄	semidirect
12. C₂³×C₈×C₄₃	C₄	semidirect
15. C₄₃×#407	C₄	semidirect
16. C₄₃×#407	C₄	semidirect
113. C₂×C₈×C₄₃	C₂²⋊C₄	semidirect
170. #10729	C₄₃	direct (N × H)
184. C₂²×C₄₃	#344	semidirect
200. C₂×#344	C₂×C₄₃	semidirect
212. C₂²×M₁₆	C₄×C₄₃	semidirect
215. C₂³×C₈	C₄×C₄₃	semidirect
218. #407	C₄×C₄₃	semidirect
219. #407	C₄×C₄₃	semidirect
226. C₄₃	#10729	direct (N × H)
317. C₂×C₈	C₂²⋊C₄×C₄₃	semidirect
387. C₂²	C₄₃×#344	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₃	2
C₂×C₄₃×#407	2
C₄₃×#2280	2
C₂×C₄₃×#344	2
#10729	43

Subgroups — C43×#10729 #24930746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10729 #24930746