Subgroups — C₄₃×#29716 #24949733

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
2	C₄₃×#2856	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1875	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₄₃	—	2	1	no	—
17	C₂×#121×C₄₃	—	2	1	no	—
18	C₂×#121×C₄₃	C₂²	1	2	yes	—
19	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#449	—	2	8	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₄₃×#391	C₂²	1	1	yes	characteristic
29	C₄₃×#391	C₂²	1	1	yes	characteristic
30	C₄₃×#390	—	2	1	no	—
31	C₄₃×#390	—	2	1	no	—
32	C₄₃×#390	C₂²	1	1	yes	characteristic
33	C₄₃×#390	C₂²	1	2	yes	—
34	C₄₃×#390	C₂²	1	1	yes	characteristic
35	C₄₃×#386	—	2	1	no	—
36	C₄₃×#386	—	2	1	no	—
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	1	yes	characteristic
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	—	4	2	no	—
46	C₂×#41×C₄₃	—	4	2	no	—
47	C₂×#41×C₄₃	D₄	1	4	yes	complemented
48	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	—	2	2	no	—
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₃	—	2	1	no	—
56	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×SD₁₆×C₄₃	—	2	4	no	—
60	C₂×SD₁₆×C₄₃	—	4	2	no	—
61	C₂×SD₁₆×C₄₃	—	4	2	no	—
62	C₂×D₈×C₄₃	—	2	4	no	—
63	C₂×D₈×C₄₃	—	4	2	no	—
64	C₂×D₈×C₄₃	—	4	2	no	—
65	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
67	#127×C₄₃	—	4	2	no	—
68	#121×C₄₃	—	2	4	no	—
69	#121×C₄₃	—	2	4	no	—
70	#121×C₄₃	—	4	4	no	—
71	#121×C₄₃	—	4	4	no	—
72	#117×C₄₃	—	4	2	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	—	4	2	no	—
88	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	—	4	2	no	—
93	#103×C₄₃	—	2	4	no	—
94	#102×C₄₃	—	2	4	no	—
95	#102×C₄₃	—	4	2	no	—
96	#102×C₄₃	—	4	2	no	—
97	C₂²⋊C₈×C₄₃	—	2	4	no	—
98	#95×C₄₃	—	2	1	no	—
99	#95×C₄₃	—	2	1	no	—
100	#95×C₄₃	—	2	1	no	—
101	#95×C₄₃	—	2	1	no	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
105	#41×C₄₃	—	4	8	no	—
106	#41×C₄₃	—	4	8	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	—	2	4	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	4	2	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂×D₄×C₄₃	—	4	4	no	—
124	C₂×D₄×C₄₃	—	4	4	no	—
125	C₂×D₄×C₄₃	—	4	2	no	—
126	C₂×D₄×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	4	2	no	—
128	C₂×D₄×C₄₃	—	4	2	no	—
129	C₂×D₄×C₄₃	—	4	2	no	—
130	C₂×D₄×C₄₃	—	4	2	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	4	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	4	1	no	—
144	C₂²×C₄×C₄₃	—	4	1	no	—
145	C₂²×C₄×C₄₃	—	4	1	no	—
146	C₂²×C₄×C₄₃	—	4	2	no	—
147	C₂²×C₄×C₄₃	—	4	2	no	—
148	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	#41	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₄₃	—	4	8	no	—
157	D₈×C₄₃	—	4	8	no	—
158	C₂×C₈×C₄₃	—	2	2	no	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	—	2	2	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	4	2	no	—
169	C₄⋊C₄×C₄₃	—	4	2	no	—
170	C₂²⋊C₄×C₄₃	—	4	2	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₂²⋊C₄×C₄₃	—	4	4	no	—
173	C₂²⋊C₄×C₄₃	—	4	4	no	—
174	C₂²⋊C₄×C₄₃	—	4	2	no	—
175	C₂²⋊C₄×C₄₃	—	4	2	no	—
176	C₂²⋊C₄×C₄₃	—	4	2	no	—
177	C₂²⋊C₄×C₄₃	—	4	4	no	—
178	C₄²×C₄₃	—	2	2	no	—
179	C₄²×C₄₃	—	2	2	no	—
180	C₄²×C₄₃	—	4	1	no	—
181	C₄²×C₄₃	—	4	1	no	—
182	C₄²×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	2	1	no	—
184	C₂³×C₄₃	—	2	1	no	—
185	C₂³×C₄₃	—	2	1	no	—
186	C₂³×C₄₃	—	2	1	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	1	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	—	4	1	no	—
195	C₂³×C₄₃	—	4	1	no	—
196	C₂³×C₄₃	—	4	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	#121	1	2	yes	—
204	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₄₃	—	2	4	no	—
206	Q₈×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	2	4	no	—
208	D₄×C₄₃	—	4	8	no	—
209	D₄×C₄₃	—	4	2	no	—
210	D₄×C₄₃	—	4	2	no	—
211	D₄×C₄₃	—	4	2	no	—
212	D₄×C₄₃	—	4	2	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	8	4	no	—
215	D₄×C₄₃	—	8	4	no	—
216	D₄×C₄₃	—	8	8	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	4	no	—
226	C₂×C₄×C₄₃	—	2	4	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	4	4	no	—
232	C₂×C₄×C₄₃	—	4	4	no	—
233	C₂×C₄×C₄₃	—	4	8	no	—
234	C₂×C₄×C₄₃	—	4	1	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	—	4	1	no	—
239	C₂×C₄×C₄₃	—	4	1	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	2	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	#121	1	2	yes	—
246	C₂×C₄×C₄₃	#135	1	2	yes	—
247	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
248	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
252	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
253	C₈×C₄₃	—	4	2	no	—
254	C₈×C₄₃	—	4	2	no	—
255	#29716	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	4	1	no	—
260	C₂²×C₄₃	—	4	1	no	—
261	C₂²×C₄₃	—	4	1	no	—
262	C₂²×C₄₃	—	4	1	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	2	no	—
265	C₂²×C₄₃	—	4	2	no	—
266	C₂²×C₄₃	—	8	1	no	—
267	C₂²×C₄₃	—	8	1	no	—
268	C₂²×C₄₃	—	8	1	no	—
269	C₂²×C₄₃	—	8	1	no	—
270	C₂²×C₄₃	—	8	2	no	—
271	C₂²×C₄₃	—	8	2	no	—
272	C₂²×C₄₃	—	8	2	no	—
273	C₂²×C₄₃	—	8	2	no	—
274	C₂²×C₄₃	—	8	2	no	—
275	C₂²×C₄₃	—	8	2	no	—
276	C₂²×C₄₃	—	8	2	no	—
277	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
278	C₂²×C₄₃	#534	1	1	yes	characteristic
279	C₂²×C₄₃	#535	1	1	yes	characteristic
280	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
281	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₄₃	#575	1	1	yes	characteristic
284	C₄×C₄₃	—	2	2	no	—
285	C₄×C₄₃	—	2	2	no	—
286	C₄×C₄₃	—	2	2	no	—
287	C₄×C₄₃	—	2	2	no	—
288	C₄×C₄₃	—	4	2	no	—
289	C₄×C₄₃	—	4	1	no	—
290	C₄×C₄₃	—	8	1	no	—
291	C₄×C₄₃	—	8	1	no	—
292	C₄×C₄₃	—	8	2	no	—
293	C₄×C₄₃	#534	1	2	yes	—
294	C₄×C₄₃	#538	1	2	yes	—
295	C₂×#449	C₂×C₄₃	1	2	yes	complemented
296	#2856	C₂×C₄₃	1	1	yes	characteristic, complemented
297	#2297	C₂×C₄₃	1	1	yes	characteristic, complemented
298	#2072	C₂×C₄₃	1	1	yes	characteristic, complemented
299	#2071	C₂×C₄₃	1	1	yes	characteristic, complemented
300	#2055	C₂×C₄₃	1	2	yes	complemented
301	#2054	C₂×C₄₃	1	2	yes	complemented
302	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
304	#1875	C₂×C₄₃	1	2	yes	complemented
305	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
306	C₂×C₄₃	—	4	2	no	—
307	C₂×C₄₃	—	8	2	no	—
308	C₂×C₄₃	—	16	2	no	—
309	C₂×C₄₃	#2617	1	1	yes	characteristic
310	C₂×C₄₃	#3035	1	1	yes	characteristic
311	C₂×C₄₃	#3038	1	1	yes	characteristic
312	C₂×C₄₃	#3188	1	1	yes	characteristic
313	C₂×C₄₃	#3194	1	1	yes	characteristic
314	C₂×C₄₃	#3207	1	1	yes	characteristic
315	C₂×C₄₃	#3214	1	1	yes	characteristic
316	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
317	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
318	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
319	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#121	—	2	1	no	—
321	C₂×#121	—	2	1	no	—
322	C₂×#121	C₂²×C₄₃	1	2	yes	—
323	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
324	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
325	#449	—	2	8	no	—
326	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
327	C₂×#103	C₂²×C₄₃	1	2	yes	—
328	C₂×#102	C₂²×C₄₃	1	2	yes	—
329	C₂×#102	C₂²×C₄₃	1	2	yes	—
330	C₂×#102	C₂²×C₄₃	1	2	yes	—
331	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
332	#391	C₂²×C₄₃	1	1	yes	characteristic
333	#391	C₂²×C₄₃	1	1	yes	characteristic
334	#390	—	2	1	no	—
335	#390	—	2	1	no	—
336	#390	C₂²×C₄₃	1	1	yes	characteristic
337	#390	C₂²×C₄₃	1	2	yes	—
338	#390	C₂²×C₄₃	1	1	yes	characteristic
339	#386	—	2	1	no	—
340	#386	—	2	1	no	—
341	#384	C₂²×C₄₃	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	—	2	1	no	—
343	C₄×C₂²⋊C₄	—	2	1	no	—
344	#340	C₂²×C₄₃	1	2	yes	—
345	#340	C₂²×C₄₃	1	2	yes	—
346	#336	C₂²×C₄₃	1	1	yes	characteristic
347	#336	C₂²×C₄₃	1	1	yes	characteristic
348	C₄₃	#29716	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#41	—	2	2	no	—
350	C₂×#41	—	4	2	no	—
351	C₂×#41	—	4	2	no	—
352	C₂×#41	D₄×C₄₃	1	4	yes	complemented
353	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
359	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
362	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	4	2	no	—
366	C₂×SD₁₆	—	4	2	no	—
367	C₂×D₈	—	2	4	no	—
368	C₂×D₈	—	4	2	no	—
369	C₂×D₈	—	4	2	no	—
370	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
371	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
372	#127	—	4	2	no	—
373	#121	—	2	4	no	—
374	#121	—	2	4	no	—
375	#121	—	4	4	no	—
376	#121	—	4	4	no	—
377	#117	—	4	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	4	2	no	—
393	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
394	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
397	C₄⋊C₈	—	4	2	no	—
398	#103	—	2	4	no	—
399	#102	—	2	4	no	—
400	#102	—	4	2	no	—
401	#102	—	4	2	no	—
402	C₂²⋊C₈	—	2	4	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
410	#41	—	4	8	no	—
411	#41	—	4	8	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
459	C₂²×C₄	#41×C₄₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
461	SD₁₆	—	4	8	no	—
462	D₈	—	4	8	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	4	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	4	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	—	4	2	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	#121×C₄₃	1	2	yes	—
509	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
510	Q₈	—	2	4	no	—
511	Q₈	—	4	2	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	8	4	no	—
520	D₄	—	8	4	no	—
521	D₄	—	8	8	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	#121×C₄₃	1	2	yes	—
551	C₂×C₄	#135×C₄₃	1	2	yes	—
552	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
553	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
556	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
557	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
558	C₈	—	4	2	no	—
559	C₈	—	4	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	2	no	—
579	C₂²	—	8	2	no	—
580	C₂²	—	8	2	no	—
581	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
582	C₂²	C₄₃×#534	1	1	yes	characteristic
583	C₂²	C₄₃×#535	1	1	yes	characteristic
584	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
585	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
586	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
587	C₂²	C₄₃×#575	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	2	no	—
597	C₄	C₄₃×#534	1	2	yes	—
598	C₄	C₄₃×#538	1	2	yes	—
599	C₂	—	4	2	no	—
600	C₂	—	8	2	no	—
601	C₂	—	16	2	no	—
602	C₂	C₄₃×#2617	1	1	yes	characteristic
603	C₂	C₄₃×#3035	1	1	yes	characteristic
604	C₂	C₄₃×#3038	1	1	yes	characteristic
605	C₂	C₄₃×#3188	1	1	yes	characteristic
606	C₂	C₄₃×#3194	1	1	yes	characteristic
607	C₂	C₄₃×#3207	1	1	yes	characteristic
608	C₂	C₄₃×#3214	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×#449	C₂	semidirect
2. C₄₃×#2856	C₂	semidirect
3. C₄₃×#2297	C₂	semidirect
4. C₄₃×#2072	C₂	semidirect
5. C₄₃×#2071	C₂	semidirect
6. C₄₃×#2055	C₂	semidirect
7. C₄₃×#2054	C₂	semidirect
8. C₄₃×#2014	C₂	semidirect
9. C₄₃×#2011	C₂	semidirect
10. C₄₃×#1875	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
47. C₂×#41×C₄₃	D₄	semidirect
255. #29716	C₄₃	direct (N × H)
295. C₂×#449	C₂×C₄₃	semidirect
296. #2856	C₂×C₄₃	semidirect
297. #2297	C₂×C₄₃	semidirect
298. #2072	C₂×C₄₃	semidirect
299. #2071	C₂×C₄₃	semidirect
300. #2055	C₂×C₄₃	semidirect
301. #2054	C₂×C₄₃	semidirect
302. #2014	C₂×C₄₃	semidirect
303. #2011	C₂×C₄₃	semidirect
304. #1875	C₂×C₄₃	semidirect
305. #1797	C₂×C₄₃	semidirect
348. C₄₃	#29716	direct (N × H)
352. C₂×#41	D₄×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×#449	2
C₄₃×#2856	2
C₄₃×#2297	2
C₄₃×#2072	2
C₄₃×#2071	2
C₄₃×#2055	2
C₄₃×#2054	2
C₄₃×#2014	2
C₄₃×#2011	2
C₄₃×#1875	2
C₄₃×#1797	2
#29716	43

Subgroups — C43×#29716 #24949733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29716 #24949733