Subgroups — C₄₃×#34985 #24955002

Order 11008.

2866 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2855	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2848	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2627	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2450	C₂	1	8	yes	maximal, complemented
8	C₄₃×#2449	C₂	1	8	yes	maximal, complemented
9	C₄₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#2308	C₂	1	2	yes	maximal
11	C₂×C₄₃×#385	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#543	—	2	8	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
20	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₄₃	—	2	8	no	—
22	C₂×C₄×D₄×C₄₃	C₂²	1	8	yes	—
23	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	complemented
25	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#400	C₂²	1	4	yes	complemented
31	C₄₃×#399	C₂²	1	4	yes	complemented
32	C₄₃×#398	C₂²	1	8	yes	complemented
33	C₄₃×#396	C₂²	1	8	yes	complemented
34	C₄₃×#395	C₂²	1	4	yes	complemented
35	C₄₃×#393	C₂²	1	4	yes	complemented
36	C₄₃×#391	C₂²	1	4	yes	complemented
37	C₄₃×#389	C₂²	1	4	yes	complemented
38	C₄₃×#387	C₂²	1	8	yes	complemented
39	C₄₃×#386	C₂²	1	4	yes	—
40	C₄₃×#386	C₂²	1	8	yes	—
41	C₄₃×#386	C₂²	1	4	yes	—
42	C₄₃×#385	C₂²	1	4	yes	—
43	C₄₃×#385	C₂²	1	4	yes	—
44	C₄₃×#385	C₂²	1	8	yes	complemented
45	C₄₃×#385	C₂²	1	8	yes	complemented
46	C₄₃×#385	C₂²	1	8	yes	complemented
47	C₄₃×#381	C₂²	1	4	yes	—
48	C₄₃×#380	C₂²	1	2	yes	—
49	C₄₃×#380	C₂²	1	2	yes	—
50	C₄₃×#380	C₂²	1	4	yes	complemented
51	C₄₃×#379	C₂²	1	4	yes	—
52	C₂×#95×C₄₃	C₂²	1	4	yes	complemented
53	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₄₃	—	2	4	no	—
58	C₂²×D₄×C₄₃	—	2	4	no	—
59	C₂²×D₄×C₄₃	Q₈	1	8	yes	complemented
60	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₄₃	—	2	4	no	—
62	C₂³×C₄×C₄₃	—	2	4	no	—
63	C₂³×C₄×C₄₃	—	4	4	no	—
64	C₂³×C₄×C₄₃	—	4	4	no	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²⋊Q₈×C₄₃	—	2	8	no	—
76	C₂²⋊Q₈×C₄₃	—	2	8	no	—
77	C₂²⋊Q₈×C₄₃	—	2	16	no	—
78	C₂²⋊Q₈×C₄₃	—	2	16	no	—
79	C₂²⋊Q₈×C₄₃	—	4	8	no	—
80	C₄×D₄×C₄₃	—	2	32	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
82	C₂×C₄⋊C₄×C₄₃	—	4	8	no	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
95	C₂×C₂²⋊C₄×C₄₃	D₄	1	8	yes	—
96	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
104	C₂×C₄²×C₄₃	—	2	4	no	—
105	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
106	#95×C₄₃	C₂³	1	8	yes	—
107	#95×C₄₃	C₂³	1	8	yes	—
108	#95×C₄₃	C₂³	1	4	yes	—
109	#95×C₄₃	C₂³	1	4	yes	—
110	#95×C₄₃	C₂³	1	8	yes	—
111	#95×C₄₃	C₂³	1	8	yes	—
112	C₂⁴×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	—	2	2	no	—
114	C₂⁴×C₄₃	—	4	2	no	—
115	C₂⁴×C₄₃	—	4	2	no	—
116	C₂⁴×C₄₃	—	4	2	no	—
117	C₂⁴×C₄₃	—	4	2	no	—
118	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
119	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
120	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
121	C₂⁴×C₄₃	#41	1	4	yes	—
122	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
123	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
125	C₂×Q₈×C₄₃	—	2	4	no	—
126	C₂×Q₈×C₄₃	—	2	4	no	—
127	C₂×Q₈×C₄₃	—	4	4	no	—
128	C₂×Q₈×C₄₃	—	4	4	no	—
129	C₂×D₄×C₄₃	—	2	32	no	—
130	C₂×D₄×C₄₃	—	2	8	no	—
131	C₂×D₄×C₄₃	—	2	8	no	—
132	C₂×D₄×C₄₃	C₂×Q₈	1	16	yes	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	8	no	—
135	C₂²×C₄×C₄₃	—	2	8	no	—
136	C₂²×C₄×C₄₃	—	2	8	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	2	no	—
140	C₂²×C₄×C₄₃	—	2	8	no	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	8	no	—
145	C₂²×C₄×C₄₃	—	4	4	no	—
146	C₂²×C₄×C₄₃	—	4	4	no	—
147	C₂²×C₄×C₄₃	—	4	2	no	—
148	C₂²×C₄×C₄₃	—	4	2	no	—
149	C₂²×C₄×C₄₃	—	4	4	no	—
150	C₂²×C₄×C₄₃	—	4	4	no	—
151	C₂²×C₄×C₄₃	—	4	2	no	—
152	C₂²×C₄×C₄₃	—	4	4	no	—
153	C₂²×C₄×C₄₃	—	4	4	no	—
154	C₂²×C₄×C₄₃	—	4	16	no	—
155	C₂²×C₄×C₄₃	—	4	16	no	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
159	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
167	C₄⋊C₄×C₄₃	—	2	8	no	—
168	C₄⋊C₄×C₄₃	—	2	8	no	—
169	C₄⋊C₄×C₄₃	—	2	4	no	—
170	C₄⋊C₄×C₄₃	—	2	4	no	—
171	C₄⋊C₄×C₄₃	—	2	8	no	—
172	C₄⋊C₄×C₄₃	—	2	16	no	—
173	C₄⋊C₄×C₄₃	—	4	8	no	—
174	C₄⋊C₄×C₄₃	—	4	4	no	—
175	C₄⋊C₄×C₄₃	—	4	4	no	—
176	C₂²⋊C₄×C₄₃	—	2	8	no	—
177	C₂²⋊C₄×C₄₃	—	2	8	no	—
178	C₂²⋊C₄×C₄₃	—	2	8	no	—
179	C₂²⋊C₄×C₄₃	—	2	8	no	—
180	C₂²⋊C₄×C₄₃	—	2	8	no	—
181	C₂²⋊C₄×C₄₃	—	4	8	no	—
182	C₂²⋊C₄×C₄₃	—	4	8	no	—
183	C₂²⋊C₄×C₄₃	C₂×D₄	1	16	yes	—
184	C₄²×C₄₃	—	2	8	no	—
185	C₂³×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	4	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	8	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	4	no	—
193	C₂³×C₄₃	—	2	4	no	—
194	C₂³×C₄₃	—	4	4	no	—
195	C₂³×C₄₃	—	4	4	no	—
196	C₂³×C₄₃	—	4	8	no	—
197	C₂³×C₄₃	—	4	8	no	—
198	C₂³×C₄₃	—	4	8	no	—
199	C₂³×C₄₃	—	4	4	no	—
200	C₂³×C₄₃	—	4	8	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	C₂²⋊Q₈	1	16	yes	complemented
203	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
204	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
205	C₂³×C₄₃	C₂²×Q₈	1	4	yes	—
206	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
207	C₂³×C₄₃	C₂²×Q₈	1	4	yes	—
208	C₂³×C₄₃	C₂×#41	1	2	yes	—
209	C₂³×C₄₃	C₂×#41	1	4	yes	—
210	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
211	Q₈×C₄₃	—	8	4	no	—
212	Q₈×C₄₃	—	8	4	no	—
213	D₄×C₄₃	—	2	32	no	—
214	C₂×C₄×C₄₃	—	2	8	no	—
215	C₂×C₄×C₄₃	—	2	8	no	—
216	C₂×C₄×C₄₃	—	2	2	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	—	2	4	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	8	no	—
226	C₂×C₄×C₄₃	—	2	8	no	—
227	C₂×C₄×C₄₃	—	2	8	no	—
228	C₂×C₄×C₄₃	—	2	4	no	—
229	C₂×C₄×C₄₃	—	2	8	no	—
230	C₂×C₄×C₄₃	—	2	8	no	—
231	C₂×C₄×C₄₃	—	4	4	no	—
232	C₂×C₄×C₄₃	—	4	4	no	—
233	C₂×C₄×C₄₃	—	4	16	no	—
234	C₂×C₄×C₄₃	—	4	16	no	—
235	C₂×C₄×C₄₃	—	4	16	no	—
236	C₂×C₄×C₄₃	—	4	4	no	—
237	C₂×C₄×C₄₃	—	8	4	no	—
238	C₂×C₄×C₄₃	—	8	4	no	—
239	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
242	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
243	#34985	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₃	—	2	4	no	—
245	C₂²×C₄₃	—	2	8	no	—
246	C₂²×C₄₃	—	2	2	no	—
247	C₂²×C₄₃	—	2	4	no	—
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	2	4	no	—
250	C₂²×C₄₃	—	2	4	no	—
251	C₂²×C₄₃	—	2	8	no	—
252	C₂²×C₄₃	—	2	4	no	—
253	C₂²×C₄₃	—	2	8	no	—
254	C₂²×C₄₃	—	4	16	no	—
255	C₂²×C₄₃	—	4	16	no	—
256	C₂²×C₄₃	—	4	4	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	4	yes	—
260	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	8	yes	—
261	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
262	C₂²×C₄₃	C₂³×Q₈	1	1	yes	characteristic
263	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
265	C₂²×C₄₃	#585	1	2	yes	—
266	C₄×C₄₃	—	2	4	no	—
267	C₄×C₄₃	—	2	4	no	—
268	C₄×C₄₃	—	2	4	no	—
269	C₄×C₄₃	—	2	4	no	—
270	C₄×C₄₃	—	4	8	no	—
271	C₄×C₄₃	—	4	2	no	—
272	C₄×C₄₃	—	4	4	no	—
273	C₄×C₄₃	—	4	4	no	—
274	C₂×#543	C₂×C₄₃	1	1	yes	characteristic, complemented
275	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
276	#2855	C₂×C₄₃	1	2	yes	complemented
277	#2848	C₂×C₄₃	1	2	yes	complemented
278	#2627	C₂×C₄₃	1	2	yes	complemented
279	#2626	C₂×C₄₃	1	2	yes	complemented
280	#2450	C₂×C₄₃	1	8	yes	complemented
281	#2449	C₂×C₄₃	1	8	yes	complemented
282	#2315	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2308	C₂×C₄₃	1	2	yes	—
284	C₂×#385	C₂×C₄₃	1	2	yes	complemented
285	C₂×C₄₃	—	2	4	no	—
286	C₂×C₄₃	—	2	8	no	—
287	C₂×C₄₃	—	4	4	no	—
288	C₂×C₄₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄₃	#3459	1	2	yes	—
290	C₂×C₄₃	#3484	1	1	yes	characteristic
291	C₂×C₄₃	#3485	1	1	yes	characteristic
292	C₂×C₄₃	#3501	1	2	yes	—
293	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
294	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
296	#543	—	2	8	no	—
297	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	complemented
300	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	complemented
301	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	complemented
302	C₂×C₄×D₄	—	2	8	no	—
303	C₂×C₄×D₄	C₂²×C₄₃	1	8	yes	—
304	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	complemented
306	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
308	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
310	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
311	#400	C₂²×C₄₃	1	4	yes	complemented
312	#399	C₂²×C₄₃	1	4	yes	complemented
313	#398	C₂²×C₄₃	1	8	yes	complemented
314	#396	C₂²×C₄₃	1	8	yes	complemented
315	#395	C₂²×C₄₃	1	4	yes	complemented
316	#393	C₂²×C₄₃	1	4	yes	complemented
317	#391	C₂²×C₄₃	1	4	yes	complemented
318	#389	C₂²×C₄₃	1	4	yes	complemented
319	#387	C₂²×C₄₃	1	8	yes	complemented
320	#386	C₂²×C₄₃	1	4	yes	—
321	#386	C₂²×C₄₃	1	8	yes	—
322	#386	C₂²×C₄₃	1	4	yes	—
323	#385	C₂²×C₄₃	1	4	yes	—
324	#385	C₂²×C₄₃	1	4	yes	—
325	#385	C₂²×C₄₃	1	8	yes	complemented
326	#385	C₂²×C₄₃	1	8	yes	complemented
327	#385	C₂²×C₄₃	1	8	yes	complemented
328	#381	C₂²×C₄₃	1	4	yes	—
329	#380	C₂²×C₄₃	1	2	yes	—
330	#380	C₂²×C₄₃	1	2	yes	—
331	#380	C₂²×C₄₃	1	4	yes	complemented
332	#379	C₂²×C₄₃	1	4	yes	—
333	C₂×#95	C₂²×C₄₃	1	4	yes	complemented
334	C₄₃	#34985	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
336	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
338	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
339	C₂²×D₄	—	2	4	no	—
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	Q₈×C₄₃	1	8	yes	complemented
342	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
343	C₂³×C₄	—	2	4	no	—
344	C₂³×C₄	—	2	4	no	—
345	C₂³×C₄	—	4	4	no	—
346	C₂³×C₄	—	4	4	no	—
347	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
349	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
350	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
353	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
354	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
355	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
357	C₂²⋊Q₈	—	2	8	no	—
358	C₂²⋊Q₈	—	2	8	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	—	2	16	no	—
361	C₂²⋊Q₈	—	4	8	no	—
362	C₄×D₄	—	2	32	no	—
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	4	8	no	—
365	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₄₃	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	D₄×C₄₃	1	8	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
386	C₂×C₄²	—	2	4	no	—
387	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
388	#95	C₂³×C₄₃	1	8	yes	—
389	#95	C₂³×C₄₃	1	8	yes	—
390	#95	C₂³×C₄₃	1	4	yes	—
391	#95	C₂³×C₄₃	1	4	yes	—
392	#95	C₂³×C₄₃	1	8	yes	—
393	#95	C₂³×C₄₃	1	8	yes	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
401	C₂⁴	C₂×Q₈×C₄₃	1	4	yes	—
402	C₂⁴	C₂×Q₈×C₄₃	1	4	yes	—
403	C₂⁴	#41×C₄₃	1	4	yes	—
404	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
405	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
406	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×D₄	—	2	32	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	C₂×Q₈×C₄₃	1	16	yes	—
415	C₂²×C₄	—	2	2	no	—
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	8	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	16	no	—
437	C₂²×C₄	—	4	16	no	—
438	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
440	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₄₃	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	16	no	—
455	C₄⋊C₄	—	4	8	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	—	4	8	no	—
465	C₂²⋊C₄	C₂×D₄×C₄₃	1	16	yes	—
466	C₄²	—	2	8	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	8	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	4	no	—
484	C₂³	C₂²⋊Q₈×C₄₃	1	16	yes	complemented
485	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
486	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
487	C₂³	C₂²×Q₈×C₄₃	1	4	yes	—
488	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
489	C₂³	C₂²×Q₈×C₄₃	1	4	yes	—
490	C₂³	C₂×#41×C₄₃	1	2	yes	—
491	C₂³	C₂×#41×C₄₃	1	4	yes	—
492	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
493	Q₈	—	8	4	no	—
494	Q₈	—	8	4	no	—
495	D₄	—	2	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	16	no	—
516	C₂×C₄	—	4	16	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	16	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
522	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
523	C₂×C₄	C₂²×Q₈×C₄₃	1	4	yes	—
524	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
525	C₂²	—	2	8	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	4	16	no	—
536	C₂²	—	4	16	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	4	yes	—
541	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	8	yes	—
542	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
543	C₂²	C₂³×Q₈×C₄₃	1	1	yes	characteristic
544	C₂²	C₂²×#41×C₄₃	1	1	yes	characteristic
545	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
546	C₂²	C₄₃×#585	1	2	yes	—
547	C₄	—	2	4	no	—
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	2	4	no	—
551	C₄	—	4	8	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₂	—	2	4	no	—
556	C₂	—	2	8	no	—
557	C₂	—	4	4	no	—
558	C₂	C₂²×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
559	C₂	C₄₃×#3459	1	2	yes	—
560	C₂	C₄₃×#3484	1	1	yes	characteristic
561	C₂	C₄₃×#3485	1	1	yes	characteristic
562	C₂	C₄₃×#3501	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#543	C₂	semidirect
3. C₄₃×#2855	C₂	semidirect
4. C₄₃×#2848	C₂	semidirect
5. C₄₃×#2627	C₂	semidirect
6. C₄₃×#2626	C₂	semidirect
7. C₄₃×#2450	C₂	semidirect
8. C₄₃×#2449	C₂	semidirect
9. C₄₃×#2315	C₂	semidirect
11. C₂×C₄₃×#385	C₂	semidirect
18. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
19. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
20. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
30. C₄₃×#400	C₂²	semidirect
31. C₄₃×#399	C₂²	semidirect
32. C₄₃×#398	C₂²	semidirect
33. C₄₃×#396	C₂²	semidirect
34. C₄₃×#395	C₂²	semidirect
35. C₄₃×#393	C₂²	semidirect
36. C₄₃×#391	C₂²	semidirect
37. C₄₃×#389	C₂²	semidirect
38. C₄₃×#387	C₂²	semidirect
44. C₄₃×#385	C₂²	semidirect
45. C₄₃×#385	C₂²	semidirect
46. C₄₃×#385	C₂²	semidirect
50. C₄₃×#380	C₂²	semidirect
52. C₂×#95×C₄₃	C₂²	semidirect
59. C₂²×D₄×C₄₃	Q₈	semidirect
202. C₂³×C₄₃	C₂²⋊Q₈	semidirect
243. #34985	C₄₃	direct (N × H)
274. C₂×#543	C₂×C₄₃	semidirect
276. #2855	C₂×C₄₃	semidirect
277. #2848	C₂×C₄₃	semidirect
278. #2627	C₂×C₄₃	semidirect
279. #2626	C₂×C₄₃	semidirect
280. #2450	C₂×C₄₃	semidirect
281. #2449	C₂×C₄₃	semidirect
282. #2315	C₂×C₄₃	semidirect
284. C₂×#385	C₂×C₄₃	semidirect
299. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
301. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
305. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
311. #400	C₂²×C₄₃	semidirect
312. #399	C₂²×C₄₃	semidirect
313. #398	C₂²×C₄₃	semidirect
314. #396	C₂²×C₄₃	semidirect
315. #395	C₂²×C₄₃	semidirect
316. #393	C₂²×C₄₃	semidirect
317. #391	C₂²×C₄₃	semidirect
318. #389	C₂²×C₄₃	semidirect
319. #387	C₂²×C₄₃	semidirect
325. #385	C₂²×C₄₃	semidirect
326. #385	C₂²×C₄₃	semidirect
327. #385	C₂²×C₄₃	semidirect
331. #380	C₂²×C₄₃	semidirect
333. C₂×#95	C₂²×C₄₃	semidirect
334. C₄₃	#34985	direct (N × H)
341. C₂²×D₄	Q₈×C₄₃	semidirect
484. C₂³	C₂²⋊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×#543	2
C₂²×C₄×D₄×C₄₃	2
C₄₃×#2855	2
C₄₃×#2848	2
C₄₃×#2627	2
C₄₃×#2626	2
C₄₃×#2450	2
C₄₃×#2449	2
C₄₃×#2315	2
C₄₃×#2308	2
C₂×C₄₃×#385	2
#34985	43

Subgroups — C43×#34985 #24955002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34985 #24955002