Subgroups — C₄₃×#29950 #24949967

Order 11008.

1124 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2093	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2067	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1852	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1786	C₂	1	2	yes	maximal
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
14	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#107×C₄₃	C₂²	1	4	yes	complemented
17	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
18	C₂×#102×C₄₃	C₂²	1	4	yes	—
19	C₂×#102×C₄₃	C₂²	1	4	yes	—
20	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#391	—	2	1	no	—
22	C₄₃×#390	—	2	1	no	—
23	C₄₃×#390	—	2	1	no	—
24	C₄₃×#390	C₂²	1	2	yes	—
25	C₄₃×#390	C₂²	1	2	yes	—
26	C₄₃×#389	—	2	1	no	—
27	C₄₃×#389	C₂²	1	2	yes	complemented
28	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
29	C₄₃×#380	—	2	1	no	—
30	C₄₃×#380	C₂²	1	2	yes	—
31	C₄₃×#340	C₂²	1	4	yes	complemented
32	C₄₃×#336	C₂²	1	2	yes	complemented
33	C₂⁵×C₄₃	—	2	1	no	—
34	C₂²×Q₈×C₄₃	—	2	1	no	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	—	2	2	no	—
37	C₂²×D₄×C₄₃	—	4	2	no	—
38	C₂²×D₄×C₄₃	—	4	2	no	—
39	C₂²×D₄×C₄₃	Q₈	1	4	yes	complemented
40	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₄₃	—	4	2	no	—
47	C₂²⋊Q₈×C₄₃	—	4	4	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
64	C₂×C₄²×C₄₃	—	4	2	no	—
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	#107×C₄₃	—	4	4	no	—
70	C₄⋊C₈×C₄₃	—	4	2	no	—
71	#102×C₄₃	—	4	4	no	—
72	#102×C₄₃	—	4	4	no	—
73	C₂²⋊C₈×C₄₃	—	2	4	no	—
74	#95×C₄₃	—	2	2	no	—
75	#95×C₄₃	—	2	2	no	—
76	C₂⁴×C₄₃	—	2	4	no	—
77	C₂⁴×C₄₃	—	2	2	no	—
78	C₂⁴×C₄₃	—	4	2	no	—
79	C₂⁴×C₄₃	—	4	2	no	—
80	C₂⁴×C₄₃	—	4	2	no	—
81	C₂⁴×C₄₃	—	4	2	no	—
82	C₂⁴×C₄₃	—	4	2	no	—
83	C₂⁴×C₄₃	—	4	2	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	—	4	2	no	—
86	C₂×Q₈×C₄₃	—	4	2	no	—
87	C₂×Q₈×C₄₃	—	4	2	no	—
88	C₂×D₄×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	4	8	no	—
93	C₂×D₄×C₄₃	—	4	8	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	2	no	—
96	C₂×D₄×C₄₃	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	4	1	no	—
105	C₂²×C₄×C₄₃	—	4	1	no	—
106	C₂²×C₄×C₄₃	—	4	1	no	—
107	C₂²×C₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	D₈	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₄₃	#41	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	4	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	4	2	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	—	4	4	no	—
129	C₄⋊C₄×C₄₃	—	4	2	no	—
130	C₂²⋊C₄×C₄₃	—	4	4	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	4	no	—
133	C₂²⋊C₄×C₄₃	—	4	4	no	—
134	C₂²⋊C₄×C₄₃	—	4	4	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	4	1	no	—
138	C₄²×C₄₃	—	4	1	no	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	4	8	no	—
145	C₂³×C₄₃	—	4	8	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	4	8	no	—
153	C₂³×C₄₃	—	8	4	no	—
154	C₂³×C₄₃	—	8	4	no	—
155	C₂³×C₄₃	—	8	4	no	—
156	C₂³×C₄₃	—	8	4	no	—
157	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
158	C₂³×C₄₃	C₂×D₈	1	2	yes	—
159	C₂³×C₄₃	#137	1	2	yes	—
160	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₃	—	8	4	no	—
162	D₄×C₄₃	—	2	8	no	—
163	D₄×C₄₃	—	4	8	no	—
164	D₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	8	4	no	—
190	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
191	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
198	C₈×C₄₃	—	4	4	no	—
199	#29950	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₃	—	2	2	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	4	4	no	—
207	C₂²×C₄₃	—	4	4	no	—
208	C₂²×C₄₃	—	4	4	no	—
209	C₂²×C₄₃	—	8	16	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	2	no	—
213	C₂²×C₄₃	—	8	2	no	—
214	C₂²×C₄₃	#474	1	4	yes	—
215	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₄₃	#534	1	1	yes	characteristic
217	C₂²×C₄₃	#535	1	1	yes	characteristic
218	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
219	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
221	C₂²×C₄₃	#575	1	1	yes	characteristic
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	1	no	—
227	C₄×C₄₃	—	8	2	no	—
228	C₄×C₄₃	—	8	2	no	—
229	C₄×C₄₃	—	8	2	no	—
230	C₄×C₄₃	#538	1	2	yes	—
231	C₄×C₄₃	#543	1	2	yes	—
232	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
233	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
234	#2093	C₂×C₄₃	1	2	yes	complemented
235	#2067	C₂×C₄₃	1	4	yes	complemented
236	#2023	C₂×C₄₃	1	2	yes	complemented
237	#1852	C₂×C₄₃	1	2	yes	complemented
238	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
239	#1786	C₂×C₄₃	1	2	yes	—
240	C₂×C₄₃	—	2	4	no	—
241	C₂×C₄₃	—	8	4	no	—
242	C₂×C₄₃	#2626	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
244	C₂×C₄₃	#3077	1	1	yes	characteristic
245	C₂×C₄₃	#3186	1	1	yes	characteristic
246	C₂×C₄₃	#3193	1	1	yes	characteristic
247	C₂×C₄₃	#3205	1	1	yes	characteristic
248	C₂×C₄₃	#3215	1	1	yes	characteristic
249	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
251	C₂×C₂²⋊Q₈	—	2	1	no	—
252	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	—	2	1	no	—
254	C₂²×C₂²⋊C₄	—	2	1	no	—
255	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
256	C₂×#107	C₂²×C₄₃	1	4	yes	complemented
257	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
258	C₂×#102	C₂²×C₄₃	1	4	yes	—
259	C₂×#102	C₂²×C₄₃	1	4	yes	—
260	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
261	#391	—	2	1	no	—
262	#390	—	2	1	no	—
263	#390	—	2	1	no	—
264	#390	C₂²×C₄₃	1	2	yes	—
265	#390	C₂²×C₄₃	1	2	yes	—
266	#389	—	2	1	no	—
267	#389	C₂²×C₄₃	1	2	yes	complemented
268	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
269	#380	—	2	1	no	—
270	#380	C₂²×C₄₃	1	2	yes	—
271	#340	C₂²×C₄₃	1	4	yes	complemented
272	#336	C₂²×C₄₃	1	2	yes	complemented
273	C₄₃	#29950	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁵	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	4	2	no	—
279	C₂²×D₄	—	4	2	no	—
280	C₂²×D₄	Q₈×C₄₃	1	4	yes	complemented
281	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
287	C₄⋊Q₈	—	4	2	no	—
288	C₂²⋊Q₈	—	4	4	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	4	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	4	4	no	—
304	C₂×C₂²⋊C₄	—	4	4	no	—
305	C₂×C₄²	—	4	2	no	—
306	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
307	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
310	#107	—	4	4	no	—
311	C₄⋊C₈	—	4	2	no	—
312	#102	—	4	4	no	—
313	#102	—	4	4	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	4	2	no	—
320	C₂⁴	—	4	2	no	—
321	C₂⁴	—	4	2	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	—	4	2	no	—
324	C₂⁴	—	4	2	no	—
325	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	C₂×Q₈×C₄₃	1	4	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	D₈×C₄₃	1	4	yes	—
352	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
358	C₂²×C₄	#41×C₄₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	8	no	—
394	C₂³	—	8	4	no	—
395	C₂³	—	8	4	no	—
396	C₂³	—	8	4	no	—
397	C₂³	—	8	4	no	—
398	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
399	C₂³	C₂×D₈×C₄₃	1	2	yes	—
400	C₂³	#137×C₄₃	1	2	yes	—
401	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
402	Q₈	—	8	4	no	—
403	D₄	—	2	8	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	4	no	—
431	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
432	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
433	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
434	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
435	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
438	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
439	C₈	—	4	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	16	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	C₄₃×#474	1	4	yes	—
455	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
456	C₂²	C₄₃×#534	1	1	yes	characteristic
457	C₂²	C₄₃×#535	1	1	yes	characteristic
458	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
459	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
460	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
461	C₂²	C₄₃×#575	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	1	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	2	no	—
469	C₄	—	8	2	no	—
470	C₄	C₄₃×#538	1	2	yes	—
471	C₄	C₄₃×#543	1	2	yes	—
472	C₂	—	2	4	no	—
473	C₂	—	8	4	no	—
474	C₂	C₄₃×#2626	1	1	yes	characteristic
475	C₂	C₂×C₄₃×#474	1	1	yes	characteristic
476	C₂	C₄₃×#3077	1	1	yes	characteristic
477	C₂	C₄₃×#3186	1	1	yes	characteristic
478	C₂	C₄₃×#3193	1	1	yes	characteristic
479	C₂	C₄₃×#3205	1	1	yes	characteristic
480	C₂	C₄₃×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×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. C₄₃×#2857	C₂	semidirect
3. C₄₃×#2093	C₂	semidirect
4. C₄₃×#2067	C₂	semidirect
5. C₄₃×#2023	C₂	semidirect
6. C₄₃×#1852	C₂	semidirect
7. C₄₃×#1797	C₂	semidirect
10. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
16. C₂×#107×C₄₃	C₂²	semidirect
17. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
27. C₄₃×#389	C₂²	semidirect
28. C₄₃×#384	C₂²	semidirect
31. C₄₃×#340	C₂²	semidirect
32. C₄₃×#336	C₂²	semidirect
39. C₂²×D₄×C₄₃	Q₈	semidirect
199. #29950	C₄₃	direct (N × H)
232. #2857	C₂×C₄₃	semidirect
234. #2093	C₂×C₄₃	semidirect
235. #2067	C₂×C₄₃	semidirect
236. #2023	C₂×C₄₃	semidirect
237. #1852	C₂×C₄₃	semidirect
238. #1797	C₂×C₄₃	semidirect
250. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
256. C₂×#107	C₂²×C₄₃	semidirect
257. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
267. #389	C₂²×C₄₃	semidirect
268. #384	C₂²×C₄₃	semidirect
271. #340	C₂²×C₄₃	semidirect
272. #336	C₂²×C₄₃	semidirect
273. C₄₃	#29950	direct (N × H)
280. C₂²×D₄	Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#2857	2
C₂×C₄₃×#390	2
C₄₃×#2093	2
C₄₃×#2067	2
C₄₃×#2023	2
C₄₃×#1852	2
C₄₃×#1797	2
C₄₃×#1786	2
#29950	43

Subgroups — C43×#29950 #24949967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29950 #24949967