Subgroups — C₄₃×#24300 #24944317

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2025	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1875	C₂	1	2	yes	maximal
10	C₄₃×#1854	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#533	—	2	4	no	—
13	C₄₃×#533	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
19	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
22	C₂×C₄×D₄×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#117×C₄₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#476	—	2	4	no	—
27	C₄₃×#474	—	2	4	no	—
28	C₂×#107×C₄₃	C₂²	1	2	yes	—
29	C₂×#106×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#390	C₂²	1	1	yes	characteristic
36	C₄₃×#389	C₂²	1	1	yes	characteristic
37	C₄₃×#388	—	2	1	no	—
38	C₄₃×#386	—	2	1	no	—
39	C₄₃×#380	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	1	no	—
50	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	—	2	1	no	—
52	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	D₄	1	4	yes	complemented
60	C₄⋊Q₈×C₄₃	D₄	1	4	yes	complemented
61	#125×C₄₃	—	2	4	no	—
62	#125×C₄₃	—	2	4	no	—
63	C₂²⋊Q₈×C₄₃	—	2	8	no	—
64	C₂²⋊Q₈×C₄₃	—	2	8	no	—
65	#121×C₄₃	—	2	2	no	—
66	#121×C₄₃	Q₈	1	4	yes	complemented
67	C₄×Q₈×C₄₃	—	2	8	no	—
68	C₄×Q₈×C₄₃	—	2	8	no	—
69	C₄×D₄×C₄₃	—	2	2	no	—
70	C₄×D₄×C₄₃	—	2	2	no	—
71	C₄×D₄×C₄₃	—	4	4	no	—
72	#117×C₄₃	—	2	4	no	—
73	#117×C₄₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	—	2	2	no	—
91	C₂×C₄²×C₄₃	—	2	2	no	—
92	C₂×C₄²×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#107×C₄₃	—	2	4	no	—
99	#106×C₄₃	—	2	4	no	—
100	C₄⋊C₈×C₄₃	—	2	2	no	—
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	#102×C₄₃	—	2	4	no	—
103	#102×C₄₃	—	2	4	no	—
104	C₂²⋊C₈×C₄₃	—	2	4	no	—
105	#95×C₄₃	—	2	1	no	—
106	#95×C₄₃	—	2	1	no	—
107	#95×C₄₃	—	2	1	no	—
108	C₂⁴×C₄₃	—	2	1	no	—
109	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₃	—	2	4	no	—
111	C₂×Q₈×C₄₃	—	2	4	no	—
112	C₂×Q₈×C₄₃	—	4	2	no	—
113	C₂×Q₈×C₄₃	—	4	2	no	—
114	C₂×Q₈×C₄₃	—	4	2	no	—
115	C₂×Q₈×C₄₃	—	4	2	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	4	no	—
118	C₂×D₄×C₄₃	—	2	1	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	2	1	no	—
121	C₂×D₄×C₄₃	—	2	1	no	—
122	C₂×D₄×C₄₃	—	4	2	no	—
123	C₂×D₄×C₄₃	—	4	2	no	—
124	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	4	1	no	—
139	C₂²×C₄×C₄₃	—	4	1	no	—
140	C₂²×C₄×C₄₃	—	4	2	no	—
141	C₂²×C₄×C₄₃	—	4	2	no	—
142	C₂²×C₄×C₄₃	—	4	2	no	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₄₃	#41	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	2	2	no	—
155	C₂×C₈×C₄₃	—	2	2	no	—
156	C₂×C₈×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	8	no	—
158	C₄⋊C₄×C₄₃	—	2	8	no	—
159	C₄⋊C₄×C₄₃	—	2	4	no	—
160	C₄⋊C₄×C₄₃	—	2	4	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	2	2	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	1	no	—
168	C₄⋊C₄×C₄₃	—	4	2	no	—
169	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
171	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
172	C₂²⋊C₄×C₄₃	—	2	8	no	—
173	C₂²⋊C₄×C₄₃	—	2	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	2	no	—
178	C₄²×C₄₃	—	2	8	no	—
179	C₄²×C₄₃	—	2	2	no	—
180	C₄²×C₄₃	—	2	2	no	—
181	C₄²×C₄₃	—	2	1	no	—
182	C₄²×C₄₃	—	2	1	no	—
183	C₄²×C₄₃	—	4	2	no	—
184	C₄²×C₄₃	C₂×D₄	1	2	yes	—
185	C₄²×C₄₃	C₂×D₄	1	2	yes	—
186	C₂³×C₄₃	—	2	1	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	1	no	—
189	C₂³×C₄₃	—	2	1	no	—
190	C₂³×C₄₃	—	2	1	no	—
191	C₂³×C₄₃	—	2	1	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	—	4	1	no	—
195	C₂³×C₄₃	—	4	1	no	—
196	C₂³×C₄₃	—	4	1	no	—
197	C₂³×C₄₃	—	4	1	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
200	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₄₃	—	4	8	no	—
202	Q₈×C₄₃	—	4	8	no	—
203	D₄×C₄₃	—	2	2	no	—
204	D₄×C₄₃	—	2	2	no	—
205	D₄×C₄₃	—	4	8	no	—
206	D₄×C₄₃	—	4	1	no	—
207	D₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	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	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	2	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	—	4	4	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	2	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	4	no	—
233	C₂×C₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	1	no	—
239	C₂×C₄×C₄₃	—	8	4	no	—
240	C₂×C₄×C₄₃	#120	1	2	yes	—
241	C₂×C₄×C₄₃	#120	1	2	yes	—
242	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
243	C₂×C₄×C₄₃	#135	1	2	yes	—
244	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
250	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₄₃	—	4	2	no	—
252	C₈×C₄₃	—	4	2	no	—
253	#24300	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	2	2	no	—
257	C₂²×C₄₃	—	4	1	no	—
258	C₂²×C₄₃	—	4	1	no	—
259	C₂²×C₄₃	—	4	1	no	—
260	C₂²×C₄₃	—	4	1	no	—
261	C₂²×C₄₃	—	4	2	no	—
262	C₂²×C₄₃	—	4	2	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	8	1	no	—
265	C₂²×C₄₃	—	8	1	no	—
266	C₂²×C₄₃	—	8	1	no	—
267	C₂²×C₄₃	—	8	1	no	—
268	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
269	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
270	C₂²×C₄₃	#536	1	1	yes	characteristic
271	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
272	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂²×C₄₃	#575	1	1	yes	characteristic
274	C₂²×C₄₃	#575	1	1	yes	characteristic
275	C₄×C₄₃	—	2	2	no	—
276	C₄×C₄₃	—	2	2	no	—
277	C₄×C₄₃	—	4	2	no	—
278	C₄×C₄₃	—	4	1	no	—
279	C₄×C₄₃	—	4	4	no	—
280	C₄×C₄₃	—	4	1	no	—
281	C₄×C₄₃	—	4	4	no	—
282	C₄×C₄₃	—	8	1	no	—
283	C₄×C₄₃	—	8	1	no	—
284	C₄×C₄₃	#449	1	4	yes	—
285	C₄×C₄₃	#548	1	1	yes	characteristic
286	C₄×C₄₃	#548	1	1	yes	characteristic
287	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
288	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
289	C₂×#533	C₂×C₄₃	1	1	yes	characteristic, complemented
290	C₂×#476	C₂×C₄₃	1	1	yes	characteristic, complemented
291	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
292	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
293	#2059	C₂×C₄₃	1	2	yes	complemented
294	#2025	C₂×C₄₃	1	2	yes	complemented
295	#1988	C₂×C₄₃	1	1	yes	characteristic, complemented
296	#1987	C₂×C₄₃	1	1	yes	characteristic, complemented
297	#1875	C₂×C₄₃	1	2	yes	—
298	#1854	C₂×C₄₃	1	2	yes	complemented
299	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
300	C₂×C₄₃	—	4	2	no	—
301	C₂×C₄₃	—	8	2	no	—
302	C₂×C₄₃	#2409	1	1	yes	characteristic
303	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
304	C₂×C₄₃	#3005	1	1	yes	characteristic
305	C₂×C₄₃	#3076	1	1	yes	characteristic
306	C₂×C₄₃	#3077	1	1	yes	characteristic
307	C₂×C₄₃	#3233	1	1	yes	characteristic
308	C₂×C₄₃	#3235	1	1	yes	characteristic
309	#533	—	2	4	no	—
310	#533	—	2	4	no	—
311	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×#125	C₂²×C₄₃	1	2	yes	—
314	C₂×C₂²⋊Q₈	—	2	1	no	—
315	C₂×C₂²⋊Q₈	—	2	1	no	—
316	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×C₄×Q₈	—	2	1	no	—
318	C₂×C₄×Q₈	—	2	1	no	—
319	C₂×C₄×D₄	—	2	1	no	—
320	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×#117	C₂²×C₄₃	1	2	yes	—
322	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
323	#476	—	2	4	no	—
324	#474	—	2	4	no	—
325	C₂×#107	C₂²×C₄₃	1	2	yes	—
326	C₂×#106	C₂²×C₄₃	1	2	yes	—
327	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
328	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
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	#390	C₂²×C₄₃	1	1	yes	characteristic
333	#389	C₂²×C₄₃	1	1	yes	characteristic
334	#388	—	2	1	no	—
335	#386	—	2	1	no	—
336	#380	C₂²×C₄₃	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	—	2	1	no	—
339	#340	C₂²×C₄₃	1	2	yes	—
340	#340	C₂²×C₄₃	1	2	yes	—
341	#340	C₂²×C₄₃	1	2	yes	—
342	#340	C₂²×C₄₃	1	2	yes	—
343	#336	C₂²×C₄₃	1	2	yes	—
344	C₄₃	#24300	1	1	yes	characteristic, direct product factor, Sylow
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
351	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
354	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	D₄×C₄₃	1	4	yes	complemented
358	C₄⋊Q₈	D₄×C₄₃	1	4	yes	complemented
359	#125	—	2	4	no	—
360	#125	—	2	4	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	C₂²⋊Q₈	—	2	8	no	—
363	#121	—	2	2	no	—
364	#121	Q₈×C₄₃	1	4	yes	complemented
365	C₄×Q₈	—	2	8	no	—
366	C₄×Q₈	—	2	8	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	4	4	no	—
370	#117	—	2	4	no	—
371	#117	—	2	4	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
393	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
396	#107	—	2	4	no	—
397	#106	—	2	4	no	—
398	C₄⋊C₈	—	2	2	no	—
399	C₄⋊C₈	—	2	2	no	—
400	#102	—	2	4	no	—
401	#102	—	2	4	no	—
402	C₂²⋊C₈	—	2	4	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	2	no	—
413	C₂×Q₈	—	4	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
447	C₂²×C₄	#41×C₄₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
468	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
469	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	4	2	no	—
482	C₄²	C₂×D₄×C₄₃	1	2	yes	—
483	C₄²	C₂×D₄×C₄₃	1	2	yes	—
484	C₂³	—	2	1	no	—
485	C₂³	—	2	1	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
498	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
499	Q₈	—	4	8	no	—
500	Q₈	—	4	8	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	#120×C₄₃	1	2	yes	—
539	C₂×C₄	#120×C₄₃	1	2	yes	—
540	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
541	C₂×C₄	#135×C₄₃	1	2	yes	—
542	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
546	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
547	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
548	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
549	C₈	—	4	2	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
566	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
567	C₂²	C₄₃×#536	1	1	yes	characteristic
568	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
569	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
570	C₂²	C₄₃×#575	1	1	yes	characteristic
571	C₂²	C₄₃×#575	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	2	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₄₃×#449	1	4	yes	—
582	C₄	C₄₃×#548	1	1	yes	characteristic
583	C₄	C₄₃×#548	1	1	yes	characteristic
584	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
585	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₄₃×#2409	1	1	yes	characteristic
589	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
590	C₂	C₄₃×#3005	1	1	yes	characteristic
591	C₂	C₄₃×#3076	1	1	yes	characteristic
592	C₂	C₄₃×#3077	1	1	yes	characteristic
593	C₂	C₄₃×#3233	1	1	yes	characteristic
594	C₂	C₄₃×#3235	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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×#533	C₂	semidirect
2. C₂×C₄₃×#476	C₂	semidirect
3. C₂×C₄₃×#474	C₂	semidirect
5. C₄₃×#2059	C₂	semidirect
6. C₄₃×#2025	C₂	semidirect
7. C₄₃×#1988	C₂	semidirect
8. C₄₃×#1987	C₂	semidirect
10. C₄₃×#1854	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
59. C₄⋊Q₈×C₄₃	D₄	semidirect
60. C₄⋊Q₈×C₄₃	D₄	semidirect
66. #121×C₄₃	Q₈	semidirect
253. #24300	C₄₃	direct (N × H)
289. C₂×#533	C₂×C₄₃	semidirect
290. C₂×#476	C₂×C₄₃	semidirect
291. C₂×#474	C₂×C₄₃	semidirect
293. #2059	C₂×C₄₃	semidirect
294. #2025	C₂×C₄₃	semidirect
295. #1988	C₂×C₄₃	semidirect
296. #1987	C₂×C₄₃	semidirect
298. #1854	C₂×C₄₃	semidirect
299. #1797	C₂×C₄₃	semidirect
344. C₄₃	#24300	direct (N × H)
357. C₄⋊Q₈	D₄×C₄₃	semidirect
358. C₄⋊Q₈	D₄×C₄₃	semidirect
364. #121	Q₈×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×#533	2
C₂×C₄₃×#476	2
C₂×C₄₃×#474	2
C₄×#121×C₄₃	2
C₄₃×#2059	2
C₄₃×#2025	2
C₄₃×#1988	2
C₄₃×#1987	2
C₄₃×#1875	2
C₄₃×#1854	2
C₄₃×#1797	2
#24300	43

Subgroups — C43×#24300 #24944317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24300 #24944317