Subgroups — C₄₃×#13814 #24933831

Order 11008.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#385	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal
4	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1436	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1436	C₂	1	2	yes	maximal, complemented
8	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1434	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#385	C₄	1	16	yes	complemented
24	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
25	C₄×C₂²⋊C₄×C₄₃	—	2	8	no	—
26	C₄×C₂²⋊C₄×C₄₃	C₄	1	8	yes	complemented
27	C₂×#95×C₄₃	—	2	4	no	—
28	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#95×C₄₃	C₂²	1	2	yes	—
32	C₂×#95×C₄₃	C₂²	1	2	yes	—
33	C₂×#95×C₄₃	C₂²	1	2	yes	—
34	C₂×#95×C₄₃	C₂²	1	2	yes	—
35	C₂×#95×C₄₃	C₂²	1	2	yes	—
36	C₂×#95×C₄₃	C₂²	1	2	yes	—
37	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
40	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	—	2	4	no	—
42	C₂³×C₄×C₄₃	—	2	4	no	—
43	C₂³×C₄×C₄₃	—	2	4	no	—
44	C₂³×C₄×C₄₃	—	2	2	no	—
45	C₂³×C₄×C₄₃	—	2	4	no	—
46	C₂³×C₄×C₄₃	—	2	2	no	—
47	C₂³×C₄×C₄₃	—	2	4	no	—
48	C₂³×C₄×C₄₃	—	4	2	no	—
49	C₂³×C₄×C₄₃	—	4	2	no	—
50	C₂³×C₄×C₄₃	—	4	2	no	—
51	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
52	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
53	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
68	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
69	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
72	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
73	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
74	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
75	C₂×C₂²⋊C₄×C₄₃	D₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₄₃	Q₈	1	4	yes	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	—	2	4	no	—
80	C₂×C₄²×C₄₃	—	2	4	no	—
81	C₂×C₄²×C₄₃	—	2	4	no	—
82	C₂×C₄²×C₄₃	—	2	4	no	—
83	C₂×C₄²×C₄₃	—	4	2	no	—
84	C₂×C₄²×C₄₃	—	4	2	no	—
85	C₂×C₄²×C₄₃	—	4	2	no	—
86	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
87	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	4	no	—
90	#95×C₄₃	—	2	4	no	—
91	#95×C₄₃	—	2	4	no	—
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	2	no	—
94	#95×C₄₃	—	4	2	no	—
95	#95×C₄₃	C₂×C₄	1	4	yes	complemented
96	#95×C₄₃	C₂×C₄	1	4	yes	complemented
97	#95×C₄₃	C₂×C₄	1	8	yes	complemented
98	#95×C₄₃	C₂×C₄	1	8	yes	complemented
99	#95×C₄₃	D₄	1	4	yes	—
100	C₂⁴×C₄₃	—	2	1	no	—
101	C₂⁴×C₄₃	—	2	2	no	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	C₂⁴×C₄₃	—	2	1	no	—
104	C₂⁴×C₄₃	—	2	2	no	—
105	C₂⁴×C₄₃	—	2	1	no	—
106	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
108	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
109	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
110	C₂⁴×C₄₃	#41	1	4	yes	—
111	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	—	2	8	no	—
113	C₂²×C₄×C₄₃	—	2	16	no	—
114	C₂²×C₄×C₄₃	—	2	8	no	—
115	C₂²×C₄×C₄₃	—	2	16	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	2	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	2	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	2	no	—
156	C₂²×C₄×C₄₃	—	4	4	no	—
157	C₂²×C₄×C₄₃	—	4	8	no	—
158	C₂²×C₄×C₄₃	—	4	8	no	—
159	C₂²×C₄×C₄₃	—	4	8	no	—
160	C₂²×C₄×C₄₃	—	4	8	no	—
161	C₂²×C₄×C₄₃	—	4	8	no	—
162	C₂²×C₄×C₄₃	—	4	8	no	—
163	C₂²×C₄×C₄₃	—	4	8	no	—
164	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
166	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
168	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
176	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
181	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
182	C₂²×C₄×C₄₃	#41	1	2	yes	—
183	C₂²×C₄×C₄₃	#41	1	4	yes	—
184	C₄⋊C₄×C₄₃	—	2	16	no	—
185	C₄⋊C₄×C₄₃	—	4	8	no	—
186	C₂²⋊C₄×C₄₃	—	2	16	no	—
187	C₂²⋊C₄×C₄₃	C₄²	1	16	yes	complemented
188	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
189	C₄²×C₄₃	—	2	8	no	—
190	C₄²×C₄₃	—	4	4	no	—
191	C₄²×C₄₃	—	4	8	no	—
192	C₄²×C₄₃	—	4	8	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	4	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	4	no	—
197	C₂³×C₄₃	—	2	2	no	—
198	C₂³×C₄₃	—	2	4	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	2	4	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	4	no	—
203	C₂³×C₄₃	—	2	4	no	—
204	C₂³×C₄₃	—	2	2	no	—
205	C₂³×C₄₃	—	2	2	no	—
206	C₂³×C₄₃	—	2	4	no	—
207	C₂³×C₄₃	—	2	4	no	—
208	C₂³×C₄₃	—	2	4	no	—
209	C₂³×C₄₃	—	2	2	no	—
210	C₂³×C₄₃	—	2	4	no	—
211	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
212	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
213	C₂³×C₄₃	#117	1	4	yes	—
214	C₂³×C₄₃	C₄×D₄	1	8	yes	—
215	C₂³×C₄₃	C₄×Q₈	1	8	yes	—
216	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
217	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
218	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
221	C₂³×C₄₃	C₂×#41	1	2	yes	—
222	C₂³×C₄₃	C₂×#41	1	2	yes	—
223	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
224	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
226	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	2	2	no	—
230	C₂×C₄×C₄₃	—	2	4	no	—
231	C₂×C₄×C₄₃	—	2	4	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	4	no	—
235	C₂×C₄×C₄₃	—	2	2	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	4	no	—
239	C₂×C₄×C₄₃	—	2	4	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	4	no	—
243	C₂×C₄×C₄₃	—	2	2	no	—
244	C₂×C₄×C₄₃	—	2	4	no	—
245	C₂×C₄×C₄₃	—	2	4	no	—
246	C₂×C₄×C₄₃	—	2	4	no	—
247	C₂×C₄×C₄₃	—	2	4	no	—
248	C₂×C₄×C₄₃	—	2	4	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	2	no	—
251	C₂×C₄×C₄₃	—	2	4	no	—
252	C₂×C₄×C₄₃	—	2	4	no	—
253	C₂×C₄×C₄₃	—	2	2	no	—
254	C₂×C₄×C₄₃	—	2	4	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	4	no	—
257	C₂×C₄×C₄₃	—	2	4	no	—
258	C₂×C₄×C₄₃	—	2	4	no	—
259	C₂×C₄×C₄₃	—	2	2	no	—
260	C₂×C₄×C₄₃	—	2	4	no	—
261	C₂×C₄×C₄₃	—	2	4	no	—
262	C₂×C₄×C₄₃	—	2	4	no	—
263	C₂×C₄×C₄₃	—	2	4	no	—
264	C₂×C₄×C₄₃	—	2	4	no	—
265	C₂×C₄×C₄₃	—	2	2	no	—
266	C₂×C₄×C₄₃	—	2	4	no	—
267	C₂×C₄×C₄₃	—	4	16	no	—
268	C₂×C₄×C₄₃	—	4	32	no	—
269	C₂×C₄×C₄₃	—	4	2	no	—
270	C₂×C₄×C₄₃	—	4	2	no	—
271	C₂×C₄×C₄₃	—	4	2	no	—
272	C₂×C₄×C₄₃	—	4	2	no	—
273	C₂×C₄×C₄₃	—	4	2	no	—
274	C₂×C₄×C₄₃	—	4	2	no	—
275	C₂×C₄×C₄₃	—	4	2	no	—
276	C₂×C₄×C₄₃	—	4	2	no	—
277	C₂×C₄×C₄₃	—	4	2	no	—
278	C₂×C₄×C₄₃	—	4	2	no	—
279	C₂×C₄×C₄₃	—	4	2	no	—
280	C₂×C₄×C₄₃	—	4	2	no	—
281	C₂×C₄×C₄₃	—	4	2	no	—
282	C₂×C₄×C₄₃	—	4	2	no	—
283	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
284	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
285	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
286	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
287	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
288	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
289	#13814	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂²×C₄₃	—	2	4	no	—
291	C₂²×C₄₃	—	2	4	no	—
292	C₂²×C₄₃	—	2	4	no	—
293	C₂²×C₄₃	—	2	4	no	—
294	C₂²×C₄₃	—	2	8	no	—
295	C₂²×C₄₃	—	2	8	no	—
296	C₂²×C₄₃	—	2	8	no	—
297	C₂²×C₄₃	—	2	8	no	—
298	C₂²×C₄₃	—	2	4	no	—
299	C₂²×C₄₃	—	2	4	no	—
300	C₂²×C₄₃	C₄×C₄⋊C₄	1	8	yes	complemented
301	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
302	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
303	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
304	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
305	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
306	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
307	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
308	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
309	C₂²×C₄₃	C₄×#41	1	2	yes	—
310	C₂²×C₄₃	#518	1	1	yes	characteristic
311	C₂²×C₄₃	#518	1	2	yes	—
312	C₂²×C₄₃	#520	1	1	yes	characteristic
313	C₂²×C₄₃	#520	1	2	yes	—
314	C₂²×C₄₃	D₄²	1	1	yes	characteristic
315	C₂²×C₄₃	#546	1	2	yes	—
316	C₂²×C₄₃	#546	1	2	yes	—
317	C₂²×C₄₃	#547	1	1	yes	characteristic
318	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
319	C₂²×C₄₃	#551	1	2	yes	—
320	C₂²×C₄₃	#551	1	2	yes	—
321	C₂²×C₄₃	#552	1	2	yes	—
322	C₂²×C₄₃	#554	1	1	yes	characteristic
323	C₂²×C₄₃	#554	1	2	yes	—
324	C₄×C₄₃	—	2	4	no	—
325	C₄×C₄₃	—	2	4	no	—
326	C₄×C₄₃	—	2	4	no	—
327	C₄×C₄₃	—	2	8	no	—
328	C₄×C₄₃	—	2	4	no	—
329	C₄×C₄₃	—	2	4	no	—
330	C₄×C₄₃	—	4	2	no	—
331	C₄×C₄₃	—	4	4	no	—
332	C₄×C₄₃	—	4	4	no	—
333	C₄×C₄₃	—	4	4	no	—
334	C₂×#385	C₂×C₄₃	1	2	yes	—
335	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
336	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	2	yes	—
337	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
338	C₂²×#95	C₂×C₄₃	1	1	yes	characteristic
339	#1436	C₂×C₄₃	1	2	yes	complemented
340	#1436	C₂×C₄₃	1	2	yes	complemented
341	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic, complemented
342	#1434	C₂×C₄₃	1	1	yes	characteristic, complemented
343	C₂²⋊#95	C₂×C₄₃	1	1	yes	characteristic
344	C₄×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
345	C₂×C₄₃	—	2	8	no	—
346	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
347	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
348	C₂×C₄₃	#2275	1	1	yes	characteristic
349	C₂×C₄₃	#2342	1	1	yes	characteristic
350	C₂×C₄₃	#2343	1	1	yes	characteristic
351	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
352	C₂×C₄₃	#2349	1	1	yes	characteristic
353	C₂×C₄₃	#2358	1	2	yes	—
354	C₂×C₄₃	#2359	1	2	yes	—
355	C₂×C₄₃	#2360	1	2	yes	—
356	C₂×C₄₃	#2368	1	2	yes	—
357	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
358	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
359	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
360	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
362	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
364	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
365	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
366	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
367	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
368	#385	C₄×C₄₃	1	16	yes	complemented
369	C₄×C₄⋊C₄	—	2	4	no	—
370	C₄×C₂²⋊C₄	—	2	8	no	—
371	C₄×C₂²⋊C₄	C₄×C₄₃	1	8	yes	complemented
372	C₂×#95	—	2	4	no	—
373	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
374	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
375	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
376	C₂×#95	C₂²×C₄₃	1	2	yes	—
377	C₂×#95	C₂²×C₄₃	1	2	yes	—
378	C₂×#95	C₂²×C₄₃	1	2	yes	—
379	C₂×#95	C₂²×C₄₃	1	2	yes	—
380	C₂×#95	C₂²×C₄₃	1	2	yes	—
381	C₂×#95	C₂²×C₄₃	1	2	yes	—
382	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
383	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
384	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
385	C₄₃	#13814	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	—	2	4	no	—
390	C₂³×C₄	—	2	2	no	—
391	C₂³×C₄	—	2	4	no	—
392	C₂³×C₄	—	2	2	no	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	4	2	no	—
395	C₂³×C₄	—	4	2	no	—
396	C₂³×C₄	—	4	2	no	—
397	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
398	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	—
399	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
400	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
401	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
402	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
408	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	—	2	4	no	—
410	C₂×C₄⋊C₄	—	2	4	no	—
411	C₂×C₄⋊C₄	—	4	2	no	—
412	C₂×C₄⋊C₄	—	4	2	no	—
413	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
414	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₂²⋊C₄	—	2	4	no	—
417	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
421	C₂×C₂²⋊C₄	D₄×C₄₃	1	4	yes	—
422	C₂×C₂²⋊C₄	Q₈×C₄₃	1	4	yes	—
423	C₂×C₄²	—	2	2	no	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	—	2	4	no	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	—	2	4	no	—
428	C₂×C₄²	—	2	4	no	—
429	C₂×C₄²	—	4	2	no	—
430	C₂×C₄²	—	4	2	no	—
431	C₂×C₄²	—	4	2	no	—
432	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	complemented
433	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	complemented
434	#95	—	2	2	no	—
435	#95	—	2	4	no	—
436	#95	—	2	4	no	—
437	#95	—	2	4	no	—
438	#95	—	2	2	no	—
439	#95	—	2	2	no	—
440	#95	—	4	2	no	—
441	#95	C₂×C₄×C₄₃	1	4	yes	complemented
442	#95	C₂×C₄×C₄₃	1	4	yes	complemented
443	#95	C₂×C₄×C₄₃	1	8	yes	complemented
444	#95	C₂×C₄×C₄₃	1	8	yes	complemented
445	#95	D₄×C₄₃	1	4	yes	—
446	C₂⁴	—	2	1	no	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	1	no	—
449	C₂⁴	—	2	1	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
453	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
454	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
455	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
456	C₂⁴	#41×C₄₃	1	4	yes	—
457	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	16	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	16	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	8	no	—
505	C₂²×C₄	—	4	8	no	—
506	C₂²×C₄	—	4	8	no	—
507	C₂²×C₄	—	4	8	no	—
508	C₂²×C₄	—	4	8	no	—
509	C₂²×C₄	—	4	8	no	—
510	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
511	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
512	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
513	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
514	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
515	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
516	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
517	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
518	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
519	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
520	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
521	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
522	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
526	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
527	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
528	C₂²×C₄	#41×C₄₃	1	2	yes	—
529	C₂²×C₄	#41×C₄₃	1	4	yes	—
530	C₄⋊C₄	—	2	16	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	—	2	16	no	—
533	C₂²⋊C₄	C₄²×C₄₃	1	16	yes	complemented
534	C₂²⋊C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
535	C₄²	—	2	8	no	—
536	C₄²	—	4	4	no	—
537	C₄²	—	4	8	no	—
538	C₄²	—	4	8	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	4	no	—
557	C₂³	C₂×C₄²×C₄₃	1	4	yes	—
558	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
559	C₂³	#117×C₄₃	1	4	yes	—
560	C₂³	C₄×D₄×C₄₃	1	8	yes	—
561	C₂³	C₄×Q₈×C₄₃	1	8	yes	—
562	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
563	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
564	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
565	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
566	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
567	C₂³	C₂×#41×C₄₃	1	2	yes	—
568	C₂³	C₂×#41×C₄₃	1	2	yes	—
569	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
570	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
571	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
572	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	4	16	no	—
614	C₂×C₄	—	4	32	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	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	C₂×C₄²×C₄₃	1	4	yes	—
630	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
631	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
632	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
633	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
634	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	8	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	C₄×C₄⋊C₄×C₄₃	1	8	yes	complemented
646	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
647	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
648	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
649	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
650	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
651	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
652	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
653	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
654	C₂²	C₄×#41×C₄₃	1	2	yes	—
655	C₂²	C₄₃×#518	1	1	yes	characteristic
656	C₂²	C₄₃×#518	1	2	yes	—
657	C₂²	C₄₃×#520	1	1	yes	characteristic
658	C₂²	C₄₃×#520	1	2	yes	—
659	C₂²	D₄²×C₄₃	1	1	yes	characteristic
660	C₂²	C₄₃×#546	1	2	yes	—
661	C₂²	C₄₃×#546	1	2	yes	—
662	C₂²	C₄₃×#547	1	1	yes	characteristic
663	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
664	C₂²	C₄₃×#551	1	2	yes	—
665	C₂²	C₄₃×#551	1	2	yes	—
666	C₂²	C₄₃×#552	1	2	yes	—
667	C₂²	C₄₃×#554	1	1	yes	characteristic
668	C₂²	C₄₃×#554	1	2	yes	—
669	C₄	—	2	4	no	—
670	C₄	—	2	4	no	—
671	C₄	—	2	4	no	—
672	C₄	—	2	8	no	—
673	C₄	—	2	4	no	—
674	C₄	—	2	4	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	4	no	—
677	C₄	—	4	4	no	—
678	C₄	—	4	4	no	—
679	C₂	—	2	8	no	—
680	C₂	C₂×C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
681	C₂	C₄²×D₄×C₄₃	1	1	yes	characteristic
682	C₂	C₄₃×#2275	1	1	yes	characteristic
683	C₂	C₄₃×#2342	1	1	yes	characteristic
684	C₂	C₄₃×#2343	1	1	yes	characteristic
685	C₂	D₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
686	C₂	C₄₃×#2349	1	1	yes	characteristic
687	C₂	C₄₃×#2358	1	2	yes	—
688	C₂	C₄₃×#2359	1	2	yes	—
689	C₂	C₄₃×#2360	1	2	yes	—
690	C₂	C₄₃×#2368	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂⁵×C₄₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊C₄×C₄₃	C₂	semidirect
6. C₄₃×#1436	C₂	semidirect
7. C₄₃×#1436	C₂	semidirect
8. C₄₃×C₄⋊#95	C₂	semidirect
9. C₄₃×#1434	C₂	semidirect
11. C₄×#95×C₄₃	C₂	semidirect
23. C₄₃×#385	C₄	semidirect
26. C₄×C₂²⋊C₄×C₄₃	C₄	semidirect
67. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
68. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
86. C₂×C₄²×C₄₃	C₂×C₄	semidirect
87. C₂×C₄²×C₄₃	C₂×C₄	semidirect
95. #95×C₄₃	C₂×C₄	semidirect
96. #95×C₄₃	C₂×C₄	semidirect
97. #95×C₄₃	C₂×C₄	semidirect
98. #95×C₄₃	C₂×C₄	semidirect
187. C₂²⋊C₄×C₄₃	C₄²	semidirect
188. C₂²⋊C₄×C₄₃	C₄⋊C₄	semidirect
289. #13814	C₄₃	direct (N × H)
300. C₂²×C₄₃	C₄×C₄⋊C₄	semidirect
335. C₂×C₄×C₄⋊C₄	C₂×C₄₃	semidirect
339. #1436	C₂×C₄₃	semidirect
340. #1436	C₂×C₄₃	semidirect
341. C₄⋊#95	C₂×C₄₃	semidirect
342. #1434	C₂×C₄₃	semidirect
344. C₄×#95	C₂×C₄₃	semidirect
368. #385	C₄×C₄₃	semidirect
371. C₄×C₂²⋊C₄	C₄×C₄₃	semidirect
385. C₄₃	#13814	direct (N × H)
413. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
414. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
432. C₂×C₄²	C₂×C₄×C₄₃	semidirect
433. C₂×C₄²	C₂×C₄×C₄₃	semidirect
441. #95	C₂×C₄×C₄₃	semidirect
442. #95	C₂×C₄×C₄₃	semidirect
443. #95	C₂×C₄×C₄₃	semidirect
444. #95	C₂×C₄×C₄₃	semidirect
533. C₂²⋊C₄	C₄²×C₄₃	semidirect
534. C₂²⋊C₄	C₄⋊C₄×C₄₃	semidirect
645. C₂²	C₄×C₄⋊C₄×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×#385	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₂²×#95×C₄₃	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄₃×#1434	2
C₄₃×C₂²⋊#95	2
C₄×#95×C₄₃	2
#13814	43

Subgroups — C43×#13814 #24933831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13814 #24933831