Subgroups — C₄₃×#29605 #24949622

Order 11008.

1268 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2616	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2001	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2001	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1825	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1780	C₂	1	1	yes	maximal, characteristic
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#536	—	2	4	no	—
16	C₄₃×#536	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
18	C₂×#124×C₄₃	—	2	1	no	—
19	C₂×#123×C₄₃	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
24	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#485	—	2	4	no	—
26	C₄₃×#451	—	2	4	no	—
27	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
38	C₄₃×#395	—	2	1	no	—
39	C₄₃×#394	—	2	2	no	—
40	C₄₃×#394	—	2	1	no	—
41	C₄₃×#380	C₂²	1	1	yes	characteristic
42	C₄₃×#380	C₂²	1	2	yes	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂²×Q₈×C₄₃	—	2	1	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	4	2	no	—
52	C₂²×Q₈×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
54	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
55	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₄₃	D₄	1	2	yes	—
58	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₄₃	—	2	4	no	—
63	C₂×Q₁₆×C₄₃	—	4	2	no	—
64	C₂×Q₁₆×C₄₃	—	4	2	no	—
65	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₄₃	—	2	8	no	—
69	#124×C₄₃	—	2	8	no	—
70	#123×C₄₃	—	2	16	no	—
71	C₂²⋊Q₈×C₄₃	—	2	4	no	—
72	C₂²⋊Q₈×C₄₃	—	2	4	no	—
73	C₂²⋊Q₈×C₄₃	—	2	4	no	—
74	C₂²⋊Q₈×C₄₃	—	2	4	no	—
75	C₂²⋊Q₈×C₄₃	—	2	2	no	—
76	C₂²⋊Q₈×C₄₃	—	2	2	no	—
77	C₂²⋊Q₈×C₄₃	—	4	2	no	—
78	C₂²⋊Q₈×C₄₃	—	4	2	no	—
79	#117×C₄₃	—	2	2	no	—
80	#117×C₄₃	D₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	—	2	1	no	—
97	#107×C₄₃	—	2	2	no	—
98	#106×C₄₃	—	2	2	no	—
99	#103×C₄₃	—	2	4	no	—
100	#103×C₄₃	—	2	2	no	—
101	#103×C₄₃	—	2	2	no	—
102	#103×C₄₃	—	4	2	no	—
103	#103×C₄₃	—	4	2	no	—
104	C₂²⋊C₈×C₄₃	—	2	2	no	—
105	C₂²⋊C₈×C₄₃	—	2	2	no	—
106	C₂²⋊C₈×C₄₃	—	4	2	no	—
107	C₂²⋊C₈×C₄₃	—	4	2	no	—
108	#95×C₄₃	—	2	2	no	—
109	#95×C₄₃	—	2	1	no	—
110	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
111	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
112	#41×C₄₃	—	4	8	no	—
113	#41×C₄₃	—	4	4	no	—
114	#41×C₄₃	—	4	4	no	—
115	C₂×Q₈×C₄₃	—	2	4	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	4	2	no	—
127	C₂×Q₈×C₄₃	—	4	8	no	—
128	C₂×Q₈×C₄₃	—	4	4	no	—
129	C₂×Q₈×C₄₃	—	4	4	no	—
130	C₂×Q₈×C₄₃	—	4	4	no	—
131	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	4	2	no	—
135	C₂×D₄×C₄₃	—	4	2	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	4	4	no	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
158	Q₁₆×C₄₃	—	4	8	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	8	no	—
167	C₄⋊C₄×C₄₃	—	2	8	no	—
168	C₄⋊C₄×C₄₃	—	2	1	no	—
169	C₄⋊C₄×C₄₃	—	2	1	no	—
170	C₄⋊C₄×C₄₃	—	2	1	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	4	4	no	—
175	C₄⋊C₄×C₄₃	—	4	2	no	—
176	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
178	C₂²⋊C₄×C₄₃	—	2	8	no	—
179	C₂²⋊C₄×C₄₃	—	2	8	no	—
180	C₂²⋊C₄×C₄₃	—	2	4	no	—
181	C₂²⋊C₄×C₄₃	—	4	4	no	—
182	C₂²⋊C₄×C₄₃	—	4	2	no	—
183	C₂²⋊C₄×C₄₃	—	8	1	no	—
184	C₂²⋊C₄×C₄₃	—	8	2	no	—
185	C₄²×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	1	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	#120	1	2	yes	—
198	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₄₃	—	2	4	no	—
200	Q₈×C₄₃	—	2	4	no	—
201	Q₈×C₄₃	—	4	8	no	—
202	Q₈×C₄₃	—	4	4	no	—
203	Q₈×C₄₃	—	4	2	no	—
204	Q₈×C₄₃	—	4	2	no	—
205	Q₈×C₄₃	—	4	2	no	—
206	Q₈×C₄₃	—	4	1	no	—
207	Q₈×C₄₃	—	4	1	no	—
208	D₄×C₄₃	—	4	4	no	—
209	D₄×C₄₃	—	4	8	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	4	8	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	#120	1	2	yes	—
239	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
242	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
243	C₈×C₄₃	—	4	2	no	—
244	C₈×C₄₃	—	4	1	no	—
245	C₈×C₄₃	—	4	1	no	—
246	#29605	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂²×C₄₃	—	2	2	no	—
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	2	2	no	—
250	C₂²×C₄₃	—	4	2	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	4	2	no	—
253	C₂²×C₄₃	—	4	2	no	—
254	C₂²×C₄₃	—	4	2	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
260	C₂²×C₄₃	#534	1	2	yes	—
261	C₂²×C₄₃	#577	1	1	yes	characteristic
262	C₂²×C₄₃	#578	1	2	yes	—
263	C₂²×C₄₃	#578	1	1	yes	characteristic
264	C₄×C₄₃	—	2	2	no	—
265	C₄×C₄₃	—	4	2	no	—
266	C₄×C₄₃	—	4	4	no	—
267	C₄×C₄₃	—	4	2	no	—
268	C₄×C₄₃	—	4	2	no	—
269	C₄×C₄₃	—	8	1	no	—
270	C₄×C₄₃	—	8	2	no	—
271	C₄×C₄₃	—	8	1	no	—
272	C₄×C₄₃	#534	1	2	yes	—
273	C₄×C₄₃	#535	1	1	yes	characteristic
274	C₄×C₄₃	#535	1	1	yes	characteristic
275	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
276	C₂×#485	C₂×C₄₃	1	1	yes	characteristic, complemented
277	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#2616	C₂×C₄₃	1	1	yes	characteristic
279	#2036	C₂×C₄₃	1	2	yes	complemented
280	#2035	C₂×C₄₃	1	2	yes	complemented
281	#2001	C₂×C₄₃	1	2	yes	complemented
282	#2001	C₂×C₄₃	1	2	yes	complemented
283	#1825	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
285	#1780	C₂×C₄₃	1	1	yes	characteristic
286	C₂×C₄₃	—	4	2	no	—
287	C₂×C₄₃	—	8	2	no	—
288	C₂×C₄₃	#2613	1	1	yes	characteristic
289	C₂×C₄₃	#3011	1	1	yes	characteristic
290	C₂×C₄₃	#3013	1	1	yes	characteristic
291	C₂×C₄₃	#3201	1	2	yes	—
292	C₂×C₄₃	#3202	1	2	yes	—
293	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
295	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
296	#536	—	2	4	no	—
297	#536	—	2	4	no	—
298	C₂×C₄⋊Q₈	—	2	1	no	—
299	C₂×#124	—	2	1	no	—
300	C₂×#123	—	2	2	no	—
301	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
302	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
304	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
305	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
306	#485	—	2	4	no	—
307	#451	—	2	4	no	—
308	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₄₃	1	2	yes	—
313	C₂×#103	C₂²×C₄₃	1	2	yes	—
314	C₂×#103	C₂²×C₄₃	1	2	yes	—
315	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
319	#395	—	2	1	no	—
320	#394	—	2	2	no	—
321	#394	—	2	1	no	—
322	#380	C₂²×C₄₃	1	1	yes	characteristic
323	#380	C₂²×C₄₃	1	2	yes	—
324	#340	C₂²×C₄₃	1	2	yes	—
325	#340	C₂²×C₄₃	1	2	yes	—
326	C₄₃	#29605	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	—	4	2	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	—	4	2	no	—
334	C₂²×Q₈	—	4	2	no	—
335	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
336	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
338	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
339	C₂²×D₄	D₄×C₄₃	1	2	yes	—
340	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂×Q₁₆	—	2	4	no	—
345	C₂×Q₁₆	—	4	2	no	—
346	C₂×Q₁₆	—	4	2	no	—
347	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
348	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
350	C₄⋊Q₈	—	2	8	no	—
351	#124	—	2	8	no	—
352	#123	—	2	16	no	—
353	C₂²⋊Q₈	—	2	4	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	—	2	4	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	4	2	no	—
360	C₂²⋊Q₈	—	4	2	no	—
361	#117	—	2	2	no	—
362	#117	D₄×C₄₃	1	4	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	#107	—	2	2	no	—
380	#106	—	2	2	no	—
381	#103	—	2	4	no	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#103	—	4	2	no	—
385	#103	—	4	2	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	C₂²⋊C₈	—	4	2	no	—
389	C₂²⋊C₈	—	4	2	no	—
390	#95	—	2	2	no	—
391	#95	—	2	1	no	—
392	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
393	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
394	#41	—	4	8	no	—
395	#41	—	4	4	no	—
396	#41	—	4	4	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
440	Q₁₆	—	4	8	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
459	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	8	1	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₄²	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	#120×C₄₃	1	2	yes	—
480	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
481	Q₈	—	2	4	no	—
482	Q₈	—	2	4	no	—
483	Q₈	—	4	8	no	—
484	Q₈	—	4	4	no	—
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	8	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	#120×C₄₃	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
523	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
524	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
525	C₈	—	4	2	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
541	C₂²	C₄₃×#534	1	2	yes	—
542	C₂²	C₄₃×#577	1	1	yes	characteristic
543	C₂²	C₄₃×#578	1	2	yes	—
544	C₂²	C₄₃×#578	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	2	no	—
552	C₄	—	8	1	no	—
553	C₄	C₄₃×#534	1	2	yes	—
554	C₄	C₄₃×#535	1	1	yes	characteristic
555	C₄	C₄₃×#535	1	1	yes	characteristic
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₄₃×#2613	1	1	yes	characteristic
559	C₂	C₄₃×#3011	1	1	yes	characteristic
560	C₂	C₄₃×#3013	1	1	yes	characteristic
561	C₂	C₄₃×#3201	1	2	yes	—
562	C₂	C₄₃×#3202	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#485	C₂	semidirect
3. C₂×C₄₃×#451	C₂	semidirect
5. C₄₃×#2036	C₂	semidirect
6. C₄₃×#2035	C₂	semidirect
7. C₄₃×#2001	C₂	semidirect
8. C₄₃×#2001	C₂	semidirect
9. C₄₃×#1825	C₂	semidirect
10. C₄₃×#1787	C₂	semidirect
246. #29605	C₄₃	direct (N × H)
276. C₂×#485	C₂×C₄₃	semidirect
277. C₂×#451	C₂×C₄₃	semidirect
279. #2036	C₂×C₄₃	semidirect
280. #2035	C₂×C₄₃	semidirect
281. #2001	C₂×C₄₃	semidirect
282. #2001	C₂×C₄₃	semidirect
283. #1825	C₂×C₄₃	semidirect
284. #1787	C₂×C₄₃	semidirect
326. C₄₃	#29605	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#536	2
C₂×C₄₃×#485	2
C₂×C₄₃×#451	2
C₄₃×#2616	2
C₄₃×#2036	2
C₄₃×#2035	2
C₄₃×#2001	2
C₄₃×#1825	2
C₄₃×#1787	2
C₄₃×#1780	2
#29605	43

Subgroups — C43×#29605 #24949622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29605 #24949622