Subgroups — C₄₃×#13788 #24933805

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#388	C₂	1	2	yes	maximal
2	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1437	C₂	1	2	yes	maximal
4	C₄₃×#1436	C₂	1	2	yes	maximal, complemented
5	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1434	C₂	1	2	yes	maximal, complemented
8	C₄₃×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄₃×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊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×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#388	C₄	1	16	yes	complemented
23	C₄×C₂²⋊C₄×C₄₃	C₄	1	8	yes	complemented
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#95×C₄₃	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	C₂²	1	2	yes	—
30	C₂×#95×C₄₃	C₂²	1	2	yes	—
31	C₂×#95×C₄₃	C₂²	1	2	yes	—
32	C₂×#95×C₄₃	C₂²	1	2	yes	—
33	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₃	C₂²	1	2	yes	—
36	C₂×#95×C₄₃	C₂²	1	2	yes	—
37	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	—	2	2	no	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂³×C₄×C₄₃	—	4	2	no	—
41	C₂³×C₄×C₄₃	—	4	2	no	—
42	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
55	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
56	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
59	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₄₃	—	4	2	no	—
61	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
63	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
64	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
65	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
66	C₂×C₄²×C₄₃	—	2	4	no	—
67	C₂×C₄²×C₄₃	—	4	2	no	—
68	C₂×C₄²×C₄₃	—	4	2	no	—
69	C₂×C₄²×C₄₃	—	4	2	no	—
70	C₂×C₄²×C₄₃	—	4	2	no	—
71	C₂×C₄²×C₄₃	—	4	2	no	—
72	C₂×C₄²×C₄₃	—	4	2	no	—
73	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
75	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	4	no	—
81	#95×C₄₃	—	4	2	no	—
82	#95×C₄₃	—	4	2	no	—
83	#95×C₄₃	—	4	2	no	—
84	#95×C₄₃	—	4	2	no	—
85	#95×C₄₃	C₂×C₄	1	4	yes	—
86	#95×C₄₃	C₂×C₄	1	4	yes	—
87	#95×C₄₃	C₂×C₄	1	8	yes	complemented
88	#95×C₄₃	C₂×C₄	1	8	yes	complemented
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	2	1	no	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	—	2	1	no	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	—	2	2	no	—
95	C₂⁴×C₄₃	—	2	2	no	—
96	C₂⁴×C₄₃	—	2	1	no	—
97	C₂⁴×C₄₃	—	2	1	no	—
98	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
99	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	1	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	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	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	1	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	1	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	4	4	no	—
146	C₂²×C₄×C₄₃	—	4	4	no	—
147	C₂²×C₄×C₄₃	—	4	8	no	—
148	C₂²×C₄×C₄₃	—	4	8	no	—
149	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
153	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₃	#41	1	2	yes	—
162	C₂²×C₄×C₄₃	#41	1	2	yes	—
163	C₂²×C₄×C₄₃	#41	1	4	yes	—
164	C₄⋊C₄×C₄₃	—	4	8	no	—
165	C₂²⋊C₄×C₄₃	—	2	8	no	—
166	C₂²⋊C₄×C₄₃	—	4	8	no	—
167	C₂²⋊C₄×C₄₃	—	4	8	no	—
168	C₂²⋊C₄×C₄₃	C₄²	1	16	yes	complemented
169	C₄²×C₄₃	—	4	4	no	—
170	C₄²×C₄₃	—	4	4	no	—
171	C₄²×C₄₃	—	4	8	no	—
172	C₄²×C₄₃	—	4	8	no	—
173	C₂³×C₄₃	—	2	2	no	—
174	C₂³×C₄₃	—	2	2	no	—
175	C₂³×C₄₃	—	2	4	no	—
176	C₂³×C₄₃	—	2	4	no	—
177	C₂³×C₄₃	—	2	4	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	2	no	—
183	C₂³×C₄₃	—	2	4	no	—
184	C₂³×C₄₃	—	2	4	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	—	4	2	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	2	no	—
191	C₂³×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	—	4	1	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
196	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
197	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
198	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
200	C₂³×C₄₃	C₂×#41	1	2	yes	—
201	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
202	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
203	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	4	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	2	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	4	no	—
221	C₂×C₄×C₄₃	—	2	4	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	4	no	—
226	C₂×C₄×C₄₃	—	2	4	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	2	4	no	—
229	C₂×C₄×C₄₃	—	2	4	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	4	no	—
232	C₂×C₄×C₄₃	—	2	4	no	—
233	C₂×C₄×C₄₃	—	2	4	no	—
234	C₂×C₄×C₄₃	—	2	4	no	—
235	C₂×C₄×C₄₃	—	2	4	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	2	4	no	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	4	16	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	2	no	—
245	C₂×C₄×C₄₃	—	4	2	no	—
246	C₂×C₄×C₄₃	—	4	2	no	—
247	C₂×C₄×C₄₃	—	4	2	no	—
248	C₂×C₄×C₄₃	—	4	2	no	—
249	C₂×C₄×C₄₃	—	4	2	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	4	2	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	4	2	no	—
254	C₂×C₄×C₄₃	—	4	2	no	—
255	C₂×C₄×C₄₃	—	4	2	no	—
256	C₂×C₄×C₄₃	—	4	2	no	—
257	C₂×C₄×C₄₃	—	4	2	no	—
258	C₂×C₄×C₄₃	—	4	2	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	2	no	—
261	C₂×C₄×C₄₃	—	4	2	no	—
262	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
263	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
264	C₂×C₄×C₄₃	#117	1	4	yes	—
265	C₂×C₄×C₄₃	#117	1	4	yes	—
266	#13788	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂²×C₄₃	—	2	4	no	—
268	C₂²×C₄₃	—	2	4	no	—
269	C₂²×C₄₃	—	2	4	no	—
270	C₂²×C₄₃	—	4	2	no	—
271	C₂²×C₄₃	—	4	2	no	—
272	C₂²×C₄₃	—	4	2	no	—
273	C₂²×C₄₃	—	4	2	no	—
274	C₂²×C₄₃	—	4	4	no	—
275	C₂²×C₄₃	—	4	4	no	—
276	C₂²×C₄₃	—	4	4	no	—
277	C₂²×C₄₃	—	4	4	no	—
278	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
279	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
280	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
281	C₂²×C₄₃	C₄×#41	1	2	yes	—
282	C₂²×C₄₃	C₄×#41	1	2	yes	—
283	C₂²×C₄₃	#518	1	1	yes	characteristic
284	C₂²×C₄₃	#518	1	1	yes	characteristic
285	C₂²×C₄₃	#518	1	2	yes	—
286	C₂²×C₄₃	#518	1	2	yes	—
287	C₂²×C₄₃	#520	1	1	yes	characteristic
288	C₂²×C₄₃	#520	1	1	yes	characteristic
289	C₂²×C₄₃	#520	1	2	yes	—
290	C₂²×C₄₃	#520	1	2	yes	—
291	C₂²×C₄₃	#538	1	2	yes	—
292	C₂²×C₄₃	#538	1	2	yes	—
293	C₂²×C₄₃	#538	1	2	yes	—
294	C₂²×C₄₃	#539	1	2	yes	—
295	C₂²×C₄₃	#540	1	1	yes	characteristic
296	C₂²×C₄₃	#540	1	2	yes	—
297	C₂²×C₄₃	#541	1	1	yes	characteristic
298	C₂²×C₄₃	#542	1	1	yes	characteristic
299	C₂²×C₄₃	#542	1	1	yes	characteristic
300	C₂²×C₄₃	#542	1	2	yes	—
301	C₄×C₄₃	—	2	4	no	—
302	C₄×C₄₃	—	2	4	no	—
303	C₄×C₄₃	—	2	4	no	—
304	C₄×C₄₃	—	2	4	no	—
305	C₄×C₄₃	—	4	2	no	—
306	C₄×C₄₃	—	4	2	no	—
307	C₄×C₄₃	—	4	4	no	—
308	C₄×C₄₃	—	4	4	no	—
309	C₄×C₄₃	—	4	4	no	—
310	C₄×C₄₃	—	4	4	no	—
311	C₂×#388	C₂×C₄₃	1	2	yes	—
312	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
313	#1437	C₂×C₄₃	1	2	yes	—
314	#1436	C₂×C₄₃	1	2	yes	complemented
315	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic, complemented
316	#1434	C₂×C₄₃	1	1	yes	characteristic, complemented
317	#1434	C₂×C₄₃	1	2	yes	complemented
318	C₂²⋊#95	C₂×C₄₃	1	1	yes	characteristic
319	C₂²⋊#95	C₂×C₄₃	1	1	yes	characteristic
320	C₄×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
321	C₄×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
322	C₂×C₄₃	—	4	4	no	—
323	C₂×C₄₃	C₄×#117	1	1	yes	characteristic
324	C₂×C₄₃	#2275	1	1	yes	characteristic
325	C₂×C₄₃	#2275	1	1	yes	characteristic
326	C₂×C₄₃	#2312	1	1	yes	characteristic
327	C₂×C₄₃	#2314	1	1	yes	characteristic
328	C₂×C₄₃	#2318	1	1	yes	characteristic
329	C₂×C₄₃	#2319	1	1	yes	characteristic
330	C₂×C₄₃	#2333	1	2	yes	—
331	C₂×C₄₃	#2334	1	2	yes	—
332	C₂×C₄₃	#2335	1	2	yes	—
333	C₂×C₄₃	#2337	1	2	yes	—
334	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
336	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
338	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
339	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
340	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
341	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
342	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
344	#388	C₄×C₄₃	1	16	yes	complemented
345	C₄×C₂²⋊C₄	C₄×C₄₃	1	8	yes	complemented
346	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
347	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
348	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
349	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
350	C₂×#95	C₂²×C₄₃	1	2	yes	—
351	C₂×#95	C₂²×C₄₃	1	2	yes	—
352	C₂×#95	C₂²×C₄₃	1	2	yes	—
353	C₂×#95	C₂²×C₄₃	1	2	yes	—
354	C₂×#95	C₂²×C₄₃	1	2	yes	—
355	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
356	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
357	C₂×#95	C₂²×C₄₃	1	2	yes	—
358	C₂×#95	C₂²×C₄₃	1	2	yes	—
359	C₄₃	#13788	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	—	4	2	no	—
364	C₂³×C₄	—	4	2	no	—
365	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
366	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
367	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
368	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
370	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	4	2	no	—
377	C₂×C₄⋊C₄	—	4	2	no	—
378	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	—	4	2	no	—
381	C₂×C₂²⋊C₄	—	4	2	no	—
382	C₂×C₂²⋊C₄	—	4	2	no	—
383	C₂×C₂²⋊C₄	—	4	2	no	—
384	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
389	C₂×C₄²	—	2	4	no	—
390	C₂×C₄²	—	4	2	no	—
391	C₂×C₄²	—	4	2	no	—
392	C₂×C₄²	—	4	2	no	—
393	C₂×C₄²	—	4	2	no	—
394	C₂×C₄²	—	4	2	no	—
395	C₂×C₄²	—	4	2	no	—
396	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
397	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
398	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	complemented
399	#95	—	2	2	no	—
400	#95	—	2	2	no	—
401	#95	—	2	2	no	—
402	#95	—	2	2	no	—
403	#95	—	2	4	no	—
404	#95	—	4	2	no	—
405	#95	—	4	2	no	—
406	#95	—	4	2	no	—
407	#95	—	4	2	no	—
408	#95	C₂×C₄×C₄₃	1	4	yes	—
409	#95	C₂×C₄×C₄₃	1	4	yes	—
410	#95	C₂×C₄×C₄₃	1	8	yes	complemented
411	#95	C₂×C₄×C₄₃	1	8	yes	complemented
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	—	2	1	no	—
417	C₂⁴	—	2	2	no	—
418	C₂⁴	—	2	2	no	—
419	C₂⁴	—	2	1	no	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
422	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
423	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	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	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	8	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	—	4	8	no	—
471	C₂²×C₄	—	4	8	no	—
472	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
475	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
476	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
477	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
478	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
479	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
480	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
481	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
482	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
483	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
484	C₂²×C₄	#41×C₄₃	1	2	yes	—
485	C₂²×C₄	#41×C₄₃	1	2	yes	—
486	C₂²×C₄	#41×C₄₃	1	4	yes	—
487	C₄⋊C₄	—	4	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	4	8	no	—
490	C₂²⋊C₄	—	4	8	no	—
491	C₂²⋊C₄	C₄²×C₄₃	1	16	yes	complemented
492	C₄²	—	4	4	no	—
493	C₄²	—	4	4	no	—
494	C₄²	—	4	8	no	—
495	C₄²	—	4	8	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	C₂×C₄²×C₄₃	1	4	yes	—
519	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
520	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
521	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
522	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
523	C₂³	C₂×#41×C₄₃	1	2	yes	—
524	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
525	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
526	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
527	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
528	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
529	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
586	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
587	C₂×C₄	#117×C₄₃	1	4	yes	—
588	C₂×C₄	#117×C₄₃	1	4	yes	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
601	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
602	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
603	C₂²	C₄×#41×C₄₃	1	2	yes	—
604	C₂²	C₄×#41×C₄₃	1	2	yes	—
605	C₂²	C₄₃×#518	1	1	yes	characteristic
606	C₂²	C₄₃×#518	1	2	yes	—
607	C₂²	C₄₃×#518	1	2	yes	—
608	C₂²	C₄₃×#518	1	1	yes	characteristic
609	C₂²	C₄₃×#520	1	1	yes	characteristic
610	C₂²	C₄₃×#520	1	2	yes	—
611	C₂²	C₄₃×#520	1	2	yes	—
612	C₂²	C₄₃×#520	1	1	yes	characteristic
613	C₂²	C₄₃×#538	1	2	yes	—
614	C₂²	C₄₃×#538	1	2	yes	—
615	C₂²	C₄₃×#538	1	2	yes	—
616	C₂²	C₄₃×#539	1	2	yes	—
617	C₂²	C₄₃×#540	1	2	yes	—
618	C₂²	C₄₃×#540	1	1	yes	characteristic
619	C₂²	C₄₃×#541	1	1	yes	characteristic
620	C₂²	C₄₃×#542	1	2	yes	—
621	C₂²	C₄₃×#542	1	1	yes	characteristic
622	C₂²	C₄₃×#542	1	1	yes	characteristic
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	4	no	—
629	C₄	—	4	4	no	—
630	C₄	—	4	4	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	2	no	—
633	C₂	—	4	4	no	—
634	C₂	C₄×#117×C₄₃	1	1	yes	characteristic
635	C₂	C₄₃×#2275	1	1	yes	characteristic
636	C₂	C₄₃×#2275	1	1	yes	characteristic
637	C₂	C₄₃×#2312	1	1	yes	characteristic
638	C₂	C₄₃×#2314	1	1	yes	characteristic
639	C₂	C₄₃×#2318	1	1	yes	characteristic
640	C₂	C₄₃×#2319	1	1	yes	characteristic
641	C₂	C₄₃×#2333	1	2	yes	—
642	C₂	C₄₃×#2334	1	2	yes	—
643	C₂	C₄₃×#2335	1	2	yes	—
644	C₂	C₄₃×#2337	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
4. C₄₃×#1436	C₂	semidirect
5. C₄₃×C₄⋊#95	C₂	semidirect
6. C₄₃×#1434	C₂	semidirect
7. C₄₃×#1434	C₂	semidirect
10. C₄×#95×C₄₃	C₂	semidirect
11. C₄×#95×C₄₃	C₂	semidirect
22. C₄₃×#388	C₄	semidirect
23. C₄×C₂²⋊C₄×C₄₃	C₄	semidirect
55. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
75. C₂×C₄²×C₄₃	C₂×C₄	semidirect
87. #95×C₄₃	C₂×C₄	semidirect
88. #95×C₄₃	C₂×C₄	semidirect
168. C₂²⋊C₄×C₄₃	C₄²	semidirect
266. #13788	C₄₃	direct (N × H)
314. #1436	C₂×C₄₃	semidirect
315. C₄⋊#95	C₂×C₄₃	semidirect
316. #1434	C₂×C₄₃	semidirect
317. #1434	C₂×C₄₃	semidirect
320. C₄×#95	C₂×C₄₃	semidirect
321. C₄×#95	C₂×C₄₃	semidirect
344. #388	C₄×C₄₃	semidirect
345. C₄×C₂²⋊C₄	C₄×C₄₃	semidirect
359. C₄₃	#13788	direct (N × H)
378. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
398. C₂×C₄²	C₂×C₄×C₄₃	semidirect
410. #95	C₂×C₄×C₄₃	semidirect
411. #95	C₂×C₄×C₄₃	semidirect
491. C₂²⋊C₄	C₄²×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×#388	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1437	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄₃×#1434	2
C₄₃×C₂²⋊#95	2
C₄×#95×C₄₃	2
#13788	43

Subgroups — C43×#13788 #24933805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13788 #24933805