Subgroups — C₄₃×#29633 #24949650

Order 11008.

1260 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#452	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2625	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1788	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#536	—	2	4	no	—
18	C₄₃×#536	—	2	4	no	—
19	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×#123×C₄₃	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#452	—	2	4	no	—
27	C₄₃×#451	—	2	4	no	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	2	yes	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#400	—	2	1	no	—
38	C₄₃×#398	—	2	1	no	—
39	C₄₃×#397	—	2	2	no	—
40	C₄₃×#391	C₂²	1	2	yes	—
41	C₄₃×#389	C₂²	1	2	yes	—
42	C₄₃×#380	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	4	2	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	D₄	1	4	yes	—
49	C₂²×Q₈×C₄₃	—	2	1	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	4	2	no	—
52	C₂²×Q₈×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
54	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₃	—	2	1	no	—
58	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	—	2	1	no	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×Q₁₆×C₄₃	—	2	4	no	—
63	C₂×Q₁₆×C₄₃	—	2	2	no	—
64	C₂×Q₁₆×C₄₃	—	4	2	no	—
65	C₂×Q₁₆×C₄₃	—	4	2	no	—
66	C₂×Q₁₆×C₄₃	—	4	2	no	—
67	C₂×SD₁₆×C₄₃	—	2	2	no	—
68	C₂×SD₁₆×C₄₃	—	4	2	no	—
69	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
72	C₄⋊Q₈×C₄₃	—	2	4	no	—
73	C₄⋊Q₈×C₄₃	—	2	4	no	—
74	#124×C₄₃	—	2	4	no	—
75	#124×C₄₃	—	2	4	no	—
76	#123×C₄₃	—	2	16	no	—
77	C₂²⋊Q₈×C₄₃	—	2	8	no	—
78	C₂²⋊Q₈×C₄₃	—	2	8	no	—
79	C₂²⋊Q₈×C₄₃	—	2	2	no	—
80	C₂²⋊Q₈×C₄₃	—	2	2	no	—
81	#117×C₄₃	—	2	2	no	—
82	#117×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
96	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
97	#103×C₄₃	—	2	4	no	—
98	#103×C₄₃	—	2	2	no	—
99	#103×C₄₃	—	4	2	no	—
100	#103×C₄₃	—	4	2	no	—
101	#103×C₄₃	—	4	2	no	—
102	#102×C₄₃	—	2	2	no	—
103	#102×C₄₃	—	4	2	no	—
104	C₂²⋊C₈×C₄₃	—	2	2	no	—
105	C₂²⋊C₈×C₄₃	—	2	2	no	—
106	#95×C₄₃	—	2	1	no	—
107	#95×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	2	no	—
109	#95×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
112	#41×C₄₃	—	4	4	no	—
113	#41×C₄₃	—	4	4	no	—
114	#41×C₄₃	—	4	8	no	—
115	C₂×Q₈×C₄₃	—	2	4	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	4	8	no	—
129	C₂×Q₈×C₄₃	—	4	4	no	—
130	C₂×Q₈×C₄₃	—	4	4	no	—
131	C₂×Q₈×C₄₃	—	4	4	no	—
132	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
133	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	4	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	4	4	no	—
139	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	4	4	no	—
150	C₂²×C₄×C₄₃	—	4	4	no	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
157	Q₁₆×C₄₃	—	4	8	no	—
158	Q₁₆×C₄₃	—	4	4	no	—
159	SD₁₆×C₄₃	—	4	4	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	2	8	no	—
168	C₄⋊C₄×C₄₃	—	2	8	no	—
169	C₄⋊C₄×C₄₃	—	2	2	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	1	no	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	4	2	no	—
176	C₄⋊C₄×C₄₃	—	8	2	no	—
177	C₂²⋊C₄×C₄₃	—	2	8	no	—
178	C₂²⋊C₄×C₄₃	—	2	8	no	—
179	C₂²⋊C₄×C₄₃	—	2	4	no	—
180	C₂²⋊C₄×C₄₃	—	4	2	no	—
181	C₂²⋊C₄×C₄₃	—	8	1	no	—
182	C₄²×C₄₃	—	2	2	no	—
183	C₄²×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	2	1	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	4	2	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	2	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	#120	1	2	yes	—
194	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₃	—	2	4	no	—
196	Q₈×C₄₃	—	2	2	no	—
197	Q₈×C₄₃	—	2	4	no	—
198	Q₈×C₄₃	—	2	2	no	—
199	Q₈×C₄₃	—	4	8	no	—
200	Q₈×C₄₃	—	4	2	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	Q₈×C₄₃	—	4	2	no	—
203	Q₈×C₄₃	—	4	1	no	—
204	Q₈×C₄₃	—	4	1	no	—
205	Q₈×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	2	2	no	—
207	D₄×C₄₃	—	2	2	no	—
208	D₄×C₄₃	—	4	8	no	—
209	D₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	4	8	no	—
222	C₂×C₄×C₄₃	—	4	8	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	4	2	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	#120	1	2	yes	—
235	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
238	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
239	C₈×C₄₃	—	4	1	no	—
240	C₈×C₄₃	—	4	1	no	—
241	C₈×C₄₃	—	4	2	no	—
242	#29633	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₃	—	2	2	no	—
244	C₂²×C₄₃	—	2	2	no	—
245	C₂²×C₄₃	—	2	2	no	—
246	C₂²×C₄₃	—	4	2	no	—
247	C₂²×C₄₃	—	4	2	no	—
248	C₂²×C₄₃	—	4	2	no	—
249	C₂²×C₄₃	—	4	2	no	—
250	C₂²×C₄₃	—	4	2	no	—
251	C₂²×C₄₃	—	8	2	no	—
252	C₂²×C₄₃	—	8	2	no	—
253	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₄₃	#535	1	2	yes	—
255	C₂²×C₄₃	#577	1	1	yes	characteristic
256	C₂²×C₄₃	#578	1	1	yes	characteristic
257	C₂²×C₄₃	#578	1	2	yes	—
258	C₄×C₄₃	—	2	2	no	—
259	C₄×C₄₃	—	4	2	no	—
260	C₄×C₄₃	—	4	4	no	—
261	C₄×C₄₃	—	4	2	no	—
262	C₄×C₄₃	—	4	2	no	—
263	C₄×C₄₃	—	8	1	no	—
264	C₄×C₄₃	—	8	2	no	—
265	C₄×C₄₃	—	8	1	no	—
266	C₄×C₄₃	#534	1	1	yes	characteristic
267	C₄×C₄₃	#534	1	1	yes	characteristic
268	C₄×C₄₃	#534	1	2	yes	—
269	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
270	C₂×#452	C₂×C₄₃	1	1	yes	characteristic
271	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
272	#2625	C₂×C₄₃	1	1	yes	characteristic, complemented
273	#2043	C₂×C₄₃	1	2	yes	complemented
274	#2042	C₂×C₄₃	1	2	yes	complemented
275	#2016	C₂×C₄₃	1	2	yes	complemented
276	#2015	C₂×C₄₃	1	2	yes	complemented
277	#1818	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1788	C₂×C₄₃	1	1	yes	characteristic
279	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×C₄₃	—	4	2	no	—
281	C₂×C₄₃	—	8	2	no	—
282	C₂×C₄₃	#2613	1	1	yes	characteristic
283	C₂×C₄₃	#3011	1	1	yes	characteristic
284	C₂×C₄₃	#3013	1	1	yes	characteristic
285	C₂×C₄₃	#3223	1	2	yes	—
286	C₂×C₄₃	#3225	1	2	yes	—
287	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
288	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
289	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
290	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
291	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
292	#536	—	2	4	no	—
293	#536	—	2	4	no	—
294	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
295	C₂×#124	C₂²×C₄₃	1	2	yes	—
296	C₂×#123	—	2	2	no	—
297	C₂×C₂²⋊Q₈	—	2	1	no	—
298	C₂×C₂²⋊Q₈	—	2	1	no	—
299	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
301	#452	—	2	4	no	—
302	#451	—	2	4	no	—
303	C₂×#103	C₂²×C₄₃	1	2	yes	—
304	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
305	C₂×#103	C₂²×C₄₃	1	2	yes	—
306	C₂×#103	C₂²×C₄₃	1	2	yes	—
307	C₂×#103	C₂²×C₄₃	1	2	yes	—
308	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×#102	C₂²×C₄₃	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
312	#400	—	2	1	no	—
313	#398	—	2	1	no	—
314	#397	—	2	2	no	—
315	#391	C₂²×C₄₃	1	2	yes	—
316	#389	C₂²×C₄₃	1	2	yes	—
317	#380	C₂²×C₄₃	1	1	yes	characteristic
318	#336	C₂²×C₄₃	1	2	yes	—
319	#336	C₂²×C₄₃	1	2	yes	—
320	C₄₃	#29633	1	1	yes	characteristic, direct product factor, Sylow
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	4	2	no	—
323	C₂×#41	—	4	2	no	—
324	C₂×#41	D₄×C₄₃	1	4	yes	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	4	2	no	—
328	C₂²×Q₈	—	4	2	no	—
329	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
330	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
332	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
338	C₂×Q₁₆	—	2	4	no	—
339	C₂×Q₁₆	—	2	2	no	—
340	C₂×Q₁₆	—	4	2	no	—
341	C₂×Q₁₆	—	4	2	no	—
342	C₂×Q₁₆	—	4	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	4	2	no	—
345	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
347	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
348	C₄⋊Q₈	—	2	4	no	—
349	C₄⋊Q₈	—	2	4	no	—
350	#124	—	2	4	no	—
351	#124	—	2	4	no	—
352	#123	—	2	16	no	—
353	C₂²⋊Q₈	—	2	8	no	—
354	C₂²⋊Q₈	—	2	8	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	#117	—	2	2	no	—
358	#117	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
372	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
373	#103	—	2	4	no	—
374	#103	—	2	2	no	—
375	#103	—	4	2	no	—
376	#103	—	4	2	no	—
377	#103	—	4	2	no	—
378	#102	—	2	2	no	—
379	#102	—	4	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	#95	—	2	1	no	—
383	#95	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	—	2	2	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
388	#41	—	4	4	no	—
389	#41	—	4	4	no	—
390	#41	—	4	8	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	4	8	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	4	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
409	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
433	Q₁₆	—	4	8	no	—
434	Q₁₆	—	4	4	no	—
435	SD₁₆	—	4	4	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	8	2	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	8	1	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	#120×C₄₃	1	2	yes	—
470	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
471	Q₈	—	2	4	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	4	8	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	2	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	#120×C₄₃	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
513	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
514	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
515	C₈	—	4	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
529	C₂²	C₄₃×#535	1	2	yes	—
530	C₂²	C₄₃×#577	1	1	yes	characteristic
531	C₂²	C₄₃×#578	1	1	yes	characteristic
532	C₂²	C₄₃×#578	1	2	yes	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	2	no	—
540	C₄	—	8	1	no	—
541	C₄	C₄₃×#534	1	1	yes	characteristic
542	C₄	C₄₃×#534	1	1	yes	characteristic
543	C₄	C₄₃×#534	1	2	yes	—
544	C₂	—	4	2	no	—
545	C₂	—	8	2	no	—
546	C₂	C₄₃×#2613	1	1	yes	characteristic
547	C₂	C₄₃×#3011	1	1	yes	characteristic
548	C₂	C₄₃×#3013	1	1	yes	characteristic
549	C₂	C₄₃×#3223	1	2	yes	—
550	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₃×#451	C₂	semidirect
4. C₄₃×#2625	C₂	semidirect
5. C₄₃×#2043	C₂	semidirect
6. C₄₃×#2042	C₂	semidirect
7. C₄₃×#2016	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#1818	C₂	semidirect
11. C₄₃×#1787	C₂	semidirect
242. #29633	C₄₃	direct (N × H)
271. C₂×#451	C₂×C₄₃	semidirect
272. #2625	C₂×C₄₃	semidirect
273. #2043	C₂×C₄₃	semidirect
274. #2042	C₂×C₄₃	semidirect
275. #2016	C₂×C₄₃	semidirect
276. #2015	C₂×C₄₃	semidirect
277. #1818	C₂×C₄₃	semidirect
279. #1787	C₂×C₄₃	semidirect
320. C₄₃	#29633	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#536	2
C₂×C₄₃×#452	2
C₂×C₄₃×#451	2
C₄₃×#2625	2
C₄₃×#2043	2
C₄₃×#2042	2
C₄₃×#2016	2
C₄₃×#2015	2
C₄₃×#1818	2
C₄₃×#1788	2
C₄₃×#1787	2
#29633	43

Subgroups — C43×#29633 #24949650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29633 #24949650