Subgroups — C₄₃×#23960 #24943977

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#102×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1999	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1874	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	—	2	1	no	—
13	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#547	—	2	4	no	—
17	C₄₃×#547	—	2	4	no	—
18	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×#123×C₄₃	—	2	1	no	—
20	C₂×#123×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
22	C₂×#121×C₄₃	C₂²	1	2	yes	—
23	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#120×C₄₃	—	2	1	no	—
26	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
30	C₄₃×#447	—	2	4	no	—
31	C₂×#102×C₄₃	—	2	4	no	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
38	C₄₃×#394	—	2	1	no	—
39	C₄₃×#392	—	2	1	no	—
40	C₄₃×#390	C₂²	1	2	yes	—
41	C₄₃×#380	C₂²	1	1	yes	characteristic
42	C₄₃×#379	—	2	1	no	—
43	C₄₃×#340	C₂²	1	2	yes	complemented
44	C₄₃×#340	C₂²	1	2	yes	complemented
45	C₄₃×#340	C₂²	1	2	yes	complemented
46	C₄₃×#336	C₂²	1	2	yes	complemented
47	C₂⁵×C₄₃	—	2	1	no	—
48	C₂×#41×C₄₃	—	2	8	no	—
49	C₂×#41×C₄₃	—	4	4	no	—
50	C₂×#41×C₄₃	—	4	4	no	—
51	C₂²×Q₈×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	—	2	4	no	—
53	C₂²×D₄×C₄₃	—	2	1	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	2	2	no	—
56	C₂²×D₄×C₄₃	—	2	2	no	—
57	C₂²×D₄×C₄₃	—	2	2	no	—
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	—	4	2	no	—
60	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	—	2	1	no	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×D₈×C₄₃	—	2	4	no	—
69	C₂×D₈×C₄₃	—	2	4	no	—
70	C₂×D₈×C₄₃	—	4	2	no	—
71	C₂²×C₈×C₄₃	—	2	2	no	—
72	C₂²×C₈×C₄₃	—	4	2	no	—
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₄₃	—	2	2	no	—
76	C₄⋊Q₈×C₄₃	—	2	2	no	—
77	#123×C₄₃	—	2	8	no	—
78	#123×C₄₃	—	2	8	no	—
79	C₂²⋊Q₈×C₄₃	—	2	8	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	—	2	2	no	—
82	#121×C₄₃	—	2	2	no	—
83	#121×C₄₃	—	2	4	no	—
84	#121×C₄₃	—	4	2	no	—
85	#121×C₄₃	D₄	1	4	yes	complemented
86	#120×C₄₃	—	4	4	no	—
87	C₄×D₄×C₄₃	—	2	2	no	—
88	C₄×D₄×C₄₃	—	2	2	no	—
89	C₄×D₄×C₄₃	—	2	2	no	—
90	C₄×D₄×C₄₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	complemented
99	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	#102×C₄₃	—	2	4	no	—
114	#102×C₄₃	—	2	4	no	—
115	#102×C₄₃	—	2	4	no	—
116	#102×C₄₃	—	4	2	no	—
117	C₂²⋊C₈×C₄₃	—	2	2	no	—
118	C₂²⋊C₈×C₄₃	—	4	2	no	—
119	#95×C₄₃	—	2	1	no	—
120	C₂⁴×C₄₃	—	2	1	no	—
121	C₂⁴×C₄₃	—	2	2	no	—
122	C₂⁴×C₄₃	—	4	4	no	—
123	C₂⁴×C₄₃	—	4	2	no	—
124	C₂⁴×C₄₃	—	4	2	no	—
125	C₂⁴×C₄₃	—	4	2	no	—
126	C₂⁴×C₄₃	—	8	2	no	—
127	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
129	#41×C₄₃	—	4	32	no	—
130	C₂×Q₈×C₄₃	—	2	4	no	—
131	C₂×Q₈×C₄₃	—	4	2	no	—
132	C₂×Q₈×C₄₃	—	4	2	no	—
133	C₂×D₄×C₄₃	—	2	4	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	4	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	8	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	—	2	2	no	—
145	C₂×D₄×C₄₃	—	2	2	no	—
146	C₂×D₄×C₄₃	—	4	4	no	—
147	C₂×D₄×C₄₃	—	4	4	no	—
148	C₂×D₄×C₄₃	—	4	2	no	—
149	C₂×D₄×C₄₃	—	4	8	no	—
150	C₂×D₄×C₄₃	—	4	4	no	—
151	C₂×D₄×C₄₃	—	4	2	no	—
152	C₂×D₄×C₄₃	—	4	2	no	—
153	C₂×D₄×C₄₃	—	4	2	no	—
154	C₂×D₄×C₄₃	—	4	4	no	—
155	C₂×D₄×C₄₃	—	4	2	no	—
156	C₂×D₄×C₄₃	—	8	2	no	—
157	C₂×D₄×C₄₃	D₈	1	4	yes	complemented
158	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₄₃	#41	1	4	yes	complemented
160	C₂²×C₄×C₄₃	—	2	2	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	4	no	—
163	C₂²×C₄×C₄₃	—	2	4	no	—
164	C₂²×C₄×C₄₃	—	2	1	no	—
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	2	no	—
167	C₂²×C₄×C₄₃	—	2	2	no	—
168	C₂²×C₄×C₄₃	—	2	4	no	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	1	no	—
171	C₂²×C₄×C₄₃	—	2	1	no	—
172	C₂²×C₄×C₄₃	—	2	2	no	—
173	C₂²×C₄×C₄₃	—	4	2	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	2	no	—
178	C₂²×C₄×C₄₃	—	4	2	no	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
186	D₈×C₄₃	—	4	8	no	—
187	C₂×C₈×C₄₃	—	2	2	no	—
188	C₂×C₈×C₄₃	—	2	2	no	—
189	C₂×C₈×C₄₃	—	2	2	no	—
190	C₂×C₈×C₄₃	—	2	2	no	—
191	C₂×C₈×C₄₃	—	2	2	no	—
192	C₂×C₈×C₄₃	—	2	2	no	—
193	C₂×C₈×C₄₃	—	4	4	no	—
194	C₄⋊C₄×C₄₃	—	2	4	no	—
195	C₄⋊C₄×C₄₃	—	2	4	no	—
196	C₄⋊C₄×C₄₃	—	2	4	no	—
197	C₄⋊C₄×C₄₃	—	2	2	no	—
198	C₄⋊C₄×C₄₃	—	2	1	no	—
199	C₄⋊C₄×C₄₃	—	2	1	no	—
200	C₄⋊C₄×C₄₃	—	2	1	no	—
201	C₄⋊C₄×C₄₃	—	2	2	no	—
202	C₄⋊C₄×C₄₃	—	2	2	no	—
203	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
204	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
206	C₂²⋊C₄×C₄₃	—	2	4	no	—
207	C₂²⋊C₄×C₄₃	—	2	4	no	—
208	C₂²⋊C₄×C₄₃	—	2	4	no	—
209	C₂²⋊C₄×C₄₃	—	2	2	no	—
210	C₂²⋊C₄×C₄₃	—	2	2	no	—
211	C₂²⋊C₄×C₄₃	—	4	4	no	—
212	C₂²⋊C₄×C₄₃	—	4	4	no	—
213	C₂²⋊C₄×C₄₃	—	4	2	no	—
214	C₂²⋊C₄×C₄₃	—	8	2	no	—
215	C₄²×C₄₃	—	2	1	no	—
216	C₄²×C₄₃	—	2	1	no	—
217	C₂³×C₄₃	—	2	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	1	no	—
220	C₂³×C₄₃	—	2	2	no	—
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	2	no	—
223	C₂³×C₄₃	—	2	2	no	—
224	C₂³×C₄₃	—	2	4	no	—
225	C₂³×C₄₃	—	4	8	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	—	4	2	no	—
228	C₂³×C₄₃	—	4	2	no	—
229	C₂³×C₄₃	—	4	2	no	—
230	C₂³×C₄₃	—	4	1	no	—
231	C₂³×C₄₃	—	4	1	no	—
232	C₂³×C₄₃	—	4	2	no	—
233	C₂³×C₄₃	—	4	2	no	—
234	C₂³×C₄₃	—	4	2	no	—
235	C₂³×C₄₃	—	4	2	no	—
236	C₂³×C₄₃	—	8	8	no	—
237	C₂³×C₄₃	—	8	8	no	—
238	C₂³×C₄₃	—	8	4	no	—
239	C₂³×C₄₃	—	8	4	no	—
240	C₂³×C₄₃	#120	1	2	yes	—
241	C₂³×C₄₃	C₂×D₈	1	2	yes	—
242	C₂³×C₄₃	C₂×D₈	1	2	yes	—
243	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
244	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₄₃	—	4	8	no	—
246	D₄×C₄₃	—	2	8	no	—
247	D₄×C₄₃	—	2	4	no	—
248	D₄×C₄₃	—	2	4	no	—
249	D₄×C₄₃	—	2	4	no	—
250	D₄×C₄₃	—	4	8	no	—
251	D₄×C₄₃	—	4	8	no	—
252	D₄×C₄₃	—	4	8	no	—
253	D₄×C₄₃	—	4	1	no	—
254	D₄×C₄₃	—	4	1	no	—
255	D₄×C₄₃	—	4	2	no	—
256	D₄×C₄₃	—	4	2	no	—
257	D₄×C₄₃	—	8	8	no	—
258	C₂×C₄×C₄₃	—	2	1	no	—
259	C₂×C₄×C₄₃	—	2	2	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	—	2	2	no	—
262	C₂×C₄×C₄₃	—	2	2	no	—
263	C₂×C₄×C₄₃	—	2	4	no	—
264	C₂×C₄×C₄₃	—	2	1	no	—
265	C₂×C₄×C₄₃	—	2	1	no	—
266	C₂×C₄×C₄₃	—	2	2	no	—
267	C₂×C₄×C₄₃	—	2	2	no	—
268	C₂×C₄×C₄₃	—	2	2	no	—
269	C₂×C₄×C₄₃	—	2	2	no	—
270	C₂×C₄×C₄₃	—	2	2	no	—
271	C₂×C₄×C₄₃	—	4	8	no	—
272	C₂×C₄×C₄₃	—	4	8	no	—
273	C₂×C₄×C₄₃	—	4	1	no	—
274	C₂×C₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	4	1	no	—
276	C₂×C₄×C₄₃	—	4	1	no	—
277	C₂×C₄×C₄₃	—	4	1	no	—
278	C₂×C₄×C₄₃	—	4	1	no	—
279	C₂×C₄×C₄₃	—	4	8	no	—
280	C₂×C₄×C₄₃	—	4	1	no	—
281	C₂×C₄×C₄₃	—	4	1	no	—
282	C₂×C₄×C₄₃	—	4	2	no	—
283	C₂×C₄×C₄₃	—	4	2	no	—
284	C₂×C₄×C₄₃	—	4	2	no	—
285	C₂×C₄×C₄₃	—	4	2	no	—
286	C₂×C₄×C₄₃	#120	1	2	yes	—
287	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
288	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
291	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
292	C₈×C₄₃	—	4	2	no	—
293	C₈×C₄₃	—	4	2	no	—
294	#23960	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₄₃	—	2	2	no	—
296	C₂²×C₄₃	—	2	2	no	—
297	C₂²×C₄₃	—	2	4	no	—
298	C₂²×C₄₃	—	2	4	no	—
299	C₂²×C₄₃	—	2	2	no	—
300	C₂²×C₄₃	—	2	4	no	—
301	C₂²×C₄₃	—	4	1	no	—
302	C₂²×C₄₃	—	4	1	no	—
303	C₂²×C₄₃	—	4	2	no	—
304	C₂²×C₄₃	—	4	4	no	—
305	C₂²×C₄₃	—	4	2	no	—
306	C₂²×C₄₃	—	4	2	no	—
307	C₂²×C₄₃	—	4	2	no	—
308	C₂²×C₄₃	—	4	4	no	—
309	C₂²×C₄₃	—	4	4	no	—
310	C₂²×C₄₃	—	8	16	no	—
311	C₂²×C₄₃	—	8	2	no	—
312	C₂²×C₄₃	—	8	2	no	—
313	C₂²×C₄₃	—	8	2	no	—
314	C₂²×C₄₃	—	8	2	no	—
315	C₂²×C₄₃	—	8	2	no	—
316	C₂²×C₄₃	—	8	2	no	—
317	C₂²×C₄₃	#447	1	4	yes	—
318	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
319	C₂²×C₄₃	#546	1	2	yes	—
320	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
321	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₂²×C₄₃	#577	1	2	yes	—
323	C₄×C₄₃	—	2	2	no	—
324	C₄×C₄₃	—	2	2	no	—
325	C₄×C₄₃	—	4	1	no	—
326	C₄×C₄₃	—	4	2	no	—
327	C₄×C₄₃	—	4	2	no	—
328	C₄×C₄₃	—	4	2	no	—
329	C₄×C₄₃	—	4	1	no	—
330	C₄×C₄₃	—	8	2	no	—
331	C₄×C₄₃	#525	1	1	yes	characteristic
332	C₄×C₄₃	#535	1	1	yes	characteristic
333	C₄×C₄₃	#546	1	2	yes	—
334	C₂×#547	C₂×C₄₃	1	1	yes	characteristic, complemented
335	C₂×#447	C₂×C₄₃	1	1	yes	characteristic, complemented
336	C₂²×#102	C₂×C₄₃	1	1	yes	characteristic, complemented
337	#2408	C₂×C₄₃	1	1	yes	characteristic, complemented
338	#2023	C₂×C₄₃	1	2	yes	complemented
339	#1999	C₂×C₄₃	1	2	yes	complemented
340	#1893	C₂×C₄₃	1	1	yes	characteristic, complemented
341	#1879	C₂×C₄₃	1	2	yes	complemented
342	#1874	C₂×C₄₃	1	2	yes	complemented
343	#1869	C₂×C₄₃	1	1	yes	characteristic, complemented
344	#1823	C₂×C₄₃	1	1	yes	characteristic, complemented
345	C₂×C₄₃	—	2	4	no	—
346	C₂×C₄₃	—	4	2	no	—
347	C₂×C₄₃	—	8	2	no	—
348	C₂×C₄₃	—	8	4	no	—
349	C₂×C₄₃	#2404	1	1	yes	characteristic
350	C₂×C₄₃	C₂×#447	1	1	yes	characteristic
351	C₂×C₄₃	#3010	1	1	yes	characteristic
352	C₂×C₄₃	#3294	1	2	yes	—
353	C₂×C₄₃	#3306	1	2	yes	—
354	C₂²×#41	—	2	1	no	—
355	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
356	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
357	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
358	#547	—	2	4	no	—
359	#547	—	2	4	no	—
360	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
361	C₂×#123	—	2	1	no	—
362	C₂×#123	—	2	1	no	—
363	C₂×C₂²⋊Q₈	—	2	1	no	—
364	C₂×#121	C₂²×C₄₃	1	2	yes	—
365	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
366	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic, complemented
367	C₂×#120	—	2	1	no	—
368	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
369	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
370	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
372	#447	—	2	4	no	—
373	C₂×#102	—	2	4	no	—
374	C₂×#102	C₂²×C₄₃	1	2	yes	—
375	C₂×#102	C₂²×C₄₃	1	2	yes	—
376	C₂×#102	C₂²×C₄₃	1	2	yes	—
377	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
378	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
380	#394	—	2	1	no	—
381	#392	—	2	1	no	—
382	#390	C₂²×C₄₃	1	2	yes	—
383	#380	C₂²×C₄₃	1	1	yes	characteristic
384	#379	—	2	1	no	—
385	#340	C₂²×C₄₃	1	2	yes	complemented
386	#340	C₂²×C₄₃	1	2	yes	complemented
387	#340	C₂²×C₄₃	1	2	yes	complemented
388	#336	C₂²×C₄₃	1	2	yes	complemented
389	C₄₃	#23960	1	1	yes	characteristic, direct product factor, Sylow
390	C₂⁵	—	2	1	no	—
391	C₂×#41	—	2	8	no	—
392	C₂×#41	—	4	4	no	—
393	C₂×#41	—	4	4	no	—
394	C₂²×Q₈	—	2	1	no	—
395	C₂²×D₄	—	2	4	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	—	2	2	no	—
399	C₂²×D₄	—	2	2	no	—
400	C₂²×D₄	—	2	2	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	4	2	no	—
403	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
405	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
406	C₂³×C₄	—	2	1	no	—
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
411	C₂×D₈	—	2	4	no	—
412	C₂×D₈	—	2	4	no	—
413	C₂×D₈	—	4	2	no	—
414	C₂²×C₈	—	2	2	no	—
415	C₂²×C₈	—	4	2	no	—
416	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
417	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
418	C₄⋊Q₈	—	2	2	no	—
419	C₄⋊Q₈	—	2	2	no	—
420	#123	—	2	8	no	—
421	#123	—	2	8	no	—
422	C₂²⋊Q₈	—	2	8	no	—
423	#121	—	2	2	no	—
424	#121	—	2	2	no	—
425	#121	—	2	2	no	—
426	#121	—	2	4	no	—
427	#121	—	4	2	no	—
428	#121	D₄×C₄₃	1	4	yes	complemented
429	#120	—	4	4	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	2	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	complemented
442	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	2	no	—
451	C₂×C₂²⋊C₄	—	2	2	no	—
452	C₂×C₂²⋊C₄	—	2	2	no	—
453	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
456	#102	—	2	4	no	—
457	#102	—	2	4	no	—
458	#102	—	2	4	no	—
459	#102	—	4	2	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	—	4	2	no	—
462	#95	—	2	1	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	—	4	4	no	—
466	C₂⁴	—	4	2	no	—
467	C₂⁴	—	4	2	no	—
468	C₂⁴	—	4	2	no	—
469	C₂⁴	—	8	2	no	—
470	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
471	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
472	#41	—	4	32	no	—
473	C₂×Q₈	—	2	4	no	—
474	C₂×Q₈	—	4	2	no	—
475	C₂×Q₈	—	4	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	8	2	no	—
500	C₂×D₄	D₈×C₄₃	1	4	yes	complemented
501	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
502	C₂×D₄	#41×C₄₃	1	4	yes	complemented
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
526	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
527	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
529	D₈	—	4	8	no	—
530	C₂×C₈	—	2	2	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	4	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
547	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
548	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	8	2	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	4	8	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	4	2	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	8	8	no	—
580	C₂³	—	8	8	no	—
581	C₂³	—	8	4	no	—
582	C₂³	—	8	4	no	—
583	C₂³	#120×C₄₃	1	2	yes	—
584	C₂³	C₂×D₈×C₄₃	1	2	yes	—
585	C₂³	C₂×D₈×C₄₃	1	2	yes	—
586	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
587	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
588	Q₈	—	4	8	no	—
589	D₄	—	2	8	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	4	8	no	—
594	D₄	—	4	8	no	—
595	D₄	—	4	8	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	2	no	—
600	D₄	—	8	8	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	8	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	8	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	#120×C₄₃	1	2	yes	—
630	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
631	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
633	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
634	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
635	C₈	—	4	2	no	—
636	C₈	—	4	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	8	16	no	—
653	C₂²	—	8	2	no	—
654	C₂²	—	8	2	no	—
655	C₂²	—	8	2	no	—
656	C₂²	—	8	2	no	—
657	C₂²	—	8	2	no	—
658	C₂²	—	8	2	no	—
659	C₂²	C₄₃×#447	1	4	yes	—
660	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
661	C₂²	C₄₃×#546	1	2	yes	—
662	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
663	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
664	C₂²	C₄₃×#577	1	2	yes	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	8	2	no	—
673	C₄	C₄₃×#525	1	1	yes	characteristic
674	C₄	C₄₃×#535	1	1	yes	characteristic
675	C₄	C₄₃×#546	1	2	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	2	no	—
678	C₂	—	8	4	no	—
679	C₂	—	8	2	no	—
680	C₂	C₄₃×#2404	1	1	yes	characteristic
681	C₂	C₂×C₄₃×#447	1	1	yes	characteristic
682	C₂	C₄₃×#3010	1	1	yes	characteristic
683	C₂	C₄₃×#3294	1	2	yes	—
684	C₂	C₄₃×#3306	1	2	yes	—

	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 ◁ C₂×C₄×D₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#547	C₂	semidirect
2. C₂×C₄₃×#447	C₂	semidirect
3. C₂²×#102×C₄₃	C₂	semidirect
4. C₄₃×#2408	C₂	semidirect
5. C₄₃×#2023	C₂	semidirect
6. C₄₃×#1999	C₂	semidirect
7. C₄₃×#1893	C₂	semidirect
8. C₄₃×#1879	C₂	semidirect
9. C₄₃×#1874	C₂	semidirect
10. C₄₃×#1869	C₂	semidirect
11. C₄₃×#1823	C₂	semidirect
18. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
24. C₂×#121×C₄₃	C₂²	semidirect
27. C₂×C₄×D₄×C₄₃	C₂²	semidirect
29. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
35. C₂×#102×C₄₃	C₂²	semidirect
37. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
43. C₄₃×#340	C₂²	semidirect
44. C₄₃×#340	C₂²	semidirect
45. C₄₃×#340	C₂²	semidirect
46. C₄₃×#336	C₂²	semidirect
85. #121×C₄₃	D₄	semidirect
98. C₂×C₄⋊C₄×C₄₃	D₄	semidirect
157. C₂×D₄×C₄₃	D₈	semidirect
159. C₂×D₄×C₄₃	#41	semidirect
294. #23960	C₄₃	direct (N × H)
334. C₂×#547	C₂×C₄₃	semidirect
335. C₂×#447	C₂×C₄₃	semidirect
336. C₂²×#102	C₂×C₄₃	semidirect
337. #2408	C₂×C₄₃	semidirect
338. #2023	C₂×C₄₃	semidirect
339. #1999	C₂×C₄₃	semidirect
340. #1893	C₂×C₄₃	semidirect
341. #1879	C₂×C₄₃	semidirect
342. #1874	C₂×C₄₃	semidirect
343. #1869	C₂×C₄₃	semidirect
344. #1823	C₂×C₄₃	semidirect
360. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
366. C₂×#121	C₂²×C₄₃	semidirect
369. C₂×C₄×D₄	C₂²×C₄₃	semidirect
371. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
377. C₂×#102	C₂²×C₄₃	semidirect
379. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
385. #340	C₂²×C₄₃	semidirect
386. #340	C₂²×C₄₃	semidirect
387. #340	C₂²×C₄₃	semidirect
388. #336	C₂²×C₄₃	semidirect
389. C₄₃	#23960	direct (N × H)
428. #121	D₄×C₄₃	semidirect
441. C₂×C₄⋊C₄	D₄×C₄₃	semidirect
500. C₂×D₄	D₈×C₄₃	semidirect
502. C₂×D₄	#41×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×#547	2
C₂×C₄₃×#447	2
C₂²×#102×C₄₃	2
C₄₃×#2408	2
C₄₃×#2023	2
C₄₃×#1999	2
C₄₃×#1893	2
C₄₃×#1879	2
C₄₃×#1874	2
C₄₃×#1869	2
C₄₃×#1823	2
#23960	43

Subgroups — C43×#23960 #24943977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23960 #24943977