Subgroups — C₄₃×#29712 #24949729

Order 11008.

1368 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#447	C₂	1	2	yes	maximal, complemented
2	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2054	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2011	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₄₃	C₂²	1	4	yes	—
11	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×#121×C₄₃	—	2	1	no	—
13	C₂×#121×C₄₃	—	2	1	no	—
14	C₂×#121×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#447	—	2	8	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
21	C₂×#102×C₄₃	C₂²	1	4	yes	—
22	C₂×#102×C₄₃	C₂²	1	4	yes	complemented
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#390	—	2	1	no	—
25	C₄₃×#390	—	2	1	no	—
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#390	—	2	1	no	—
28	C₄₃×#390	C₂²	1	2	yes	—
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#390	C₂²	1	2	yes	complemented
31	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
32	C₄₃×#340	C₂²	1	4	yes	complemented
33	C₄₃×#336	C₂²	1	2	yes	complemented
34	C₂⁵×C₄₃	—	2	1	no	—
35	C₂²×D₄×C₄₃	—	2	2	no	—
36	C₂²×D₄×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	—	2	1	no	—
39	C₂²×D₄×C₄₃	—	2	2	no	—
40	C₂²×D₄×C₄₃	—	4	2	no	—
41	C₂²×D₄×C₄₃	—	4	2	no	—
42	C₂²×D₄×C₄₃	D₄	1	4	yes	complemented
43	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₄₃	—	2	8	no	—
50	C₂×D₈×C₄₃	—	4	4	no	—
51	C₂×D₈×C₄₃	—	4	4	no	—
52	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
53	#127×C₄₃	—	4	2	no	—
54	#121×C₄₃	—	2	4	no	—
55	#121×C₄₃	—	2	4	no	—
56	#121×C₄₃	—	4	4	no	—
57	#121×C₄₃	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
73	C₂×C₄²×C₄₃	—	4	2	no	—
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₃	—	4	2	no	—
79	#102×C₄₃	—	2	8	no	—
80	#102×C₄₃	—	4	4	no	—
81	C₂²⋊C₈×C₄₃	—	2	4	no	—
82	C₂⁴×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	—	4	2	no	—
86	C₂⁴×C₄₃	—	4	2	no	—
87	C₂⁴×C₄₃	—	4	2	no	—
88	C₂⁴×C₄₃	—	4	2	no	—
89	C₂⁴×C₄₃	—	4	2	no	—
90	C₂⁴×C₄₃	—	4	2	no	—
91	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	2	no	—
96	C₂×D₄×C₄₃	—	2	4	no	—
97	C₂×D₄×C₄₃	—	2	4	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	4	8	no	—
101	C₂×D₄×C₄₃	—	4	8	no	—
102	C₂×D₄×C₄₃	—	4	2	no	—
103	C₂×D₄×C₄₃	—	4	2	no	—
104	C₂×D₄×C₄₃	—	4	2	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	—	4	2	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	4	2	no	—
109	C₂×D₄×C₄₃	—	4	2	no	—
110	C₂×D₄×C₄₃	—	4	4	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	4	4	no	—
113	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	4	1	no	—
121	C₂²×C₄×C₄₃	—	4	1	no	—
122	C₂²×C₄×C₄₃	—	4	1	no	—
123	C₂²×C₄×C₄₃	—	4	2	no	—
124	C₂²×C₄×C₄₃	—	4	2	no	—
125	C₂²×C₄×C₄₃	—	4	2	no	—
126	C₂²×C₄×C₄₃	D₈	1	4	yes	complemented
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	#41	1	2	yes	—
134	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
135	D₈×C₄₃	—	4	16	no	—
136	C₂×C₈×C₄₃	—	2	4	no	—
137	C₂×C₈×C₄₃	—	2	4	no	—
138	C₂×C₈×C₄₃	—	2	4	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	4	2	no	—
144	C₄⋊C₄×C₄₃	—	4	2	no	—
145	C₂²⋊C₄×C₄₃	—	4	4	no	—
146	C₂²⋊C₄×C₄₃	—	4	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	4	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	4	4	no	—
150	C₂²⋊C₄×C₄₃	—	4	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	4	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	4	1	no	—
155	C₄²×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	4	no	—
161	C₂³×C₄₃	—	4	8	no	—
162	C₂³×C₄₃	—	4	8	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	8	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	2	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	2	no	—
177	C₂³×C₄₃	—	8	4	no	—
178	C₂³×C₄₃	—	8	4	no	—
179	C₂³×C₄₃	—	8	4	no	—
180	C₂³×C₄₃	—	8	4	no	—
181	C₂³×C₄₃	#121	1	2	yes	—
182	C₂³×C₄₃	C₂×D₈	1	2	yes	—
183	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	D₄×C₄₃	—	2	8	no	—
186	D₄×C₄₃	—	4	8	no	—
187	D₄×C₄₃	—	4	4	no	—
188	D₄×C₄₃	—	4	4	no	—
189	D₄×C₄₃	—	4	4	no	—
190	D₄×C₄₃	—	8	4	no	—
191	D₄×C₄₃	—	8	4	no	—
192	D₄×C₄₃	—	8	8	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	4	4	no	—
207	C₂×C₄×C₄₃	—	4	4	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	8	4	no	—
215	C₂×C₄×C₄₃	#121	1	2	yes	—
216	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
217	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
222	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
223	C₈×C₄₃	—	4	4	no	—
224	#29712	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	—	2	2	no	—
229	C₂²×C₄₃	—	2	2	no	—
230	C₂²×C₄₃	—	2	2	no	—
231	C₂²×C₄₃	—	4	4	no	—
232	C₂²×C₄₃	—	4	4	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	—	8	16	no	—
235	C₂²×C₄₃	—	8	2	no	—
236	C₂²×C₄₃	—	8	2	no	—
237	C₂²×C₄₃	—	8	2	no	—
238	C₂²×C₄₃	—	8	2	no	—
239	C₂²×C₄₃	—	8	2	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	—	8	2	no	—
242	C₂²×C₄₃	—	8	2	no	—
243	C₂²×C₄₃	—	8	2	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	8	2	no	—
246	C₂²×C₄₃	#459	1	4	yes	—
247	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
248	C₂²×C₄₃	#534	1	1	yes	characteristic
249	C₂²×C₄₃	#535	1	1	yes	characteristic
250	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
251	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×C₄₃	#575	1	1	yes	characteristic
254	C₄×C₄₃	—	2	2	no	—
255	C₄×C₄₃	—	2	2	no	—
256	C₄×C₄₃	—	2	2	no	—
257	C₄×C₄₃	—	2	2	no	—
258	C₄×C₄₃	—	4	1	no	—
259	C₄×C₄₃	—	8	2	no	—
260	C₄×C₄₃	—	8	2	no	—
261	C₄×C₄₃	#534	1	2	yes	—
262	C₄×C₄₃	#538	1	2	yes	—
263	C₂×#447	C₂×C₄₃	1	2	yes	complemented
264	#2856	C₂×C₄₃	1	1	yes	characteristic, complemented
265	C₂×#390	C₂×C₄₃	1	1	yes	characteristic, complemented
266	#2071	C₂×C₄₃	1	2	yes	complemented
267	#2054	C₂×C₄₃	1	4	yes	complemented
268	#2011	C₂×C₄₃	1	2	yes	complemented
269	#1874	C₂×C₄₃	1	2	yes	complemented
270	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
271	C₂×C₄₃	—	2	4	no	—
272	C₂×C₄₃	—	8	4	no	—
273	C₂×C₄₃	—	16	2	no	—
274	C₂×C₄₃	#2617	1	1	yes	characteristic
275	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
276	C₂×C₄₃	#3036	1	1	yes	characteristic
277	C₂×C₄₃	#3186	1	1	yes	characteristic
278	C₂×C₄₃	#3192	1	1	yes	characteristic
279	C₂×C₄₃	#3205	1	1	yes	characteristic
280	C₂×C₄₃	#3213	1	1	yes	characteristic
281	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
282	C₂²×D₈	C₂²×C₄₃	1	4	yes	—
283	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic, complemented
284	C₂×#121	—	2	1	no	—
285	C₂×#121	—	2	1	no	—
286	C₂×#121	C₂²×C₄₃	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
288	C₂²×C₂²⋊C₄	—	2	1	no	—
289	C₂²×C₂²⋊C₄	—	2	1	no	—
290	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
291	#447	—	2	8	no	—
292	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
293	C₂×#102	C₂²×C₄₃	1	4	yes	—
294	C₂×#102	C₂²×C₄₃	1	4	yes	complemented
295	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
296	#390	—	2	1	no	—
297	#390	—	2	1	no	—
298	#390	—	2	1	no	—
299	#390	—	2	1	no	—
300	#390	C₂²×C₄₃	1	2	yes	—
301	#390	C₂²×C₄₃	1	2	yes	—
302	#390	C₂²×C₄₃	1	2	yes	complemented
303	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
304	#340	C₂²×C₄₃	1	4	yes	complemented
305	#336	C₂²×C₄₃	1	2	yes	complemented
306	C₄₃	#29712	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁵	—	2	1	no	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	4	2	no	—
314	C₂²×D₄	—	4	2	no	—
315	C₂²×D₄	D₄×C₄₃	1	4	yes	complemented
316	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
317	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
320	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
322	C₂×D₈	—	2	8	no	—
323	C₂×D₈	—	4	4	no	—
324	C₂×D₈	—	4	4	no	—
325	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
326	#127	—	4	2	no	—
327	#121	—	2	4	no	—
328	#121	—	2	4	no	—
329	#121	—	4	4	no	—
330	#121	—	4	4	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	4	2	no	—
335	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	4	4	no	—
345	C₂×C₂²⋊C₄	—	4	4	no	—
346	C₂×C₄²	—	4	2	no	—
347	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
351	C₄⋊C₈	—	4	2	no	—
352	#102	—	2	8	no	—
353	#102	—	4	4	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	4	2	no	—
359	C₂⁴	—	4	2	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	2	no	—
363	C₂⁴	—	4	2	no	—
364	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	—	4	8	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	D₈×C₄₃	1	4	yes	complemented
400	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
406	C₂²×C₄	#41×C₄₃	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
408	D₈	—	4	16	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	8	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	8	4	no	—
451	C₂³	—	8	4	no	—
452	C₂³	—	8	4	no	—
453	C₂³	—	8	4	no	—
454	C₂³	#121×C₄₃	1	2	yes	—
455	C₂³	C₂×D₈×C₄₃	1	2	yes	—
456	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
457	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
458	D₄	—	2	8	no	—
459	D₄	—	4	8	no	—
460	D₄	—	4	4	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	4	no	—
463	D₄	—	8	4	no	—
464	D₄	—	8	4	no	—
465	D₄	—	8	8	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	8	4	no	—
488	C₂×C₄	#121×C₄₃	1	2	yes	—
489	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
490	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
491	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
494	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
495	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
496	C₈	—	4	4	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	8	16	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	C₄₃×#459	1	4	yes	—
519	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
520	C₂²	C₄₃×#534	1	1	yes	characteristic
521	C₂²	C₄₃×#535	1	1	yes	characteristic
522	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
523	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
524	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
525	C₂²	C₄₃×#575	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	2	no	—
533	C₄	C₄₃×#534	1	2	yes	—
534	C₄	C₄₃×#538	1	2	yes	—
535	C₂	—	2	4	no	—
536	C₂	—	8	4	no	—
537	C₂	—	16	2	no	—
538	C₂	C₄₃×#2617	1	1	yes	characteristic
539	C₂	C₂×C₄₃×#459	1	1	yes	characteristic
540	C₂	C₄₃×#3036	1	1	yes	characteristic
541	C₂	C₄₃×#3186	1	1	yes	characteristic
542	C₂	C₄₃×#3192	1	1	yes	characteristic
543	C₂	C₄₃×#3205	1	1	yes	characteristic
544	C₂	C₄₃×#3213	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#447	C₂	semidirect
2. C₄₃×#2856	C₂	semidirect
3. C₂×C₄₃×#390	C₂	semidirect
4. C₄₃×#2071	C₂	semidirect
5. C₄₃×#2054	C₂	semidirect
6. C₄₃×#2011	C₂	semidirect
7. C₄₃×#1874	C₂	semidirect
8. C₄₃×#1797	C₂	semidirect
11. C₂×#127×C₄₃	C₂²	semidirect
20. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
22. C₂×#102×C₄₃	C₂²	semidirect
30. C₄₃×#390	C₂²	semidirect
31. C₄₃×#384	C₂²	semidirect
32. C₄₃×#340	C₂²	semidirect
33. C₄₃×#336	C₂²	semidirect
42. C₂²×D₄×C₄₃	D₄	semidirect
126. C₂²×C₄×C₄₃	D₈	semidirect
224. #29712	C₄₃	direct (N × H)
263. C₂×#447	C₂×C₄₃	semidirect
264. #2856	C₂×C₄₃	semidirect
265. C₂×#390	C₂×C₄₃	semidirect
266. #2071	C₂×C₄₃	semidirect
267. #2054	C₂×C₄₃	semidirect
268. #2011	C₂×C₄₃	semidirect
269. #1874	C₂×C₄₃	semidirect
270. #1797	C₂×C₄₃	semidirect
283. C₂×#127	C₂²×C₄₃	semidirect
292. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
294. C₂×#102	C₂²×C₄₃	semidirect
302. #390	C₂²×C₄₃	semidirect
303. #384	C₂²×C₄₃	semidirect
304. #340	C₂²×C₄₃	semidirect
305. #336	C₂²×C₄₃	semidirect
306. C₄₃	#29712	direct (N × H)
315. C₂²×D₄	D₄×C₄₃	semidirect
399. C₂²×C₄	D₈×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×#447	2
C₄₃×#2856	2
C₂×C₄₃×#390	2
C₄₃×#2071	2
C₄₃×#2054	2
C₄₃×#2011	2
C₄₃×#1874	2
C₄₃×#1797	2
#29712	43

Subgroups — C43×#29712 #24949729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29712 #24949729