Subgroups — C₄₃×#17066 #24937083

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 472 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	1	yes	maximal, characteristic
2	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1442	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1442	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1441	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1439	C₂	1	2	yes	maximal
7	C₄₃×#1439	C₂	1	2	yes	maximal
8	C₄₃×#1439	C₂	1	2	yes	maximal
9	C₄₃×#1434	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
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	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#388	—	2	4	no	—
20	C₄₃×#384	—	2	4	no	—
21	C₂×#95×C₄₃	C₂²	1	2	yes	—
22	C₂×#95×C₄₃	C₂²	1	2	yes	—
23	C₂×#95×C₄₃	C₂²	1	2	yes	—
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₃	C₂²	1	4	yes	—
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	4	yes	—
29	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
46	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
53	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
54	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
55	C₂×C₂²⋊C₄×C₄₃	Q₈	1	4	yes	—
56	C₂×C₄²×C₄₃	—	2	4	no	—
57	C₂×C₄²×C₄₃	D₄	1	4	yes	—
58	#95×C₄₃	—	2	2	no	—
59	#95×C₄₃	—	2	2	no	—
60	#95×C₄₃	—	2	4	no	—
61	#95×C₄₃	—	2	4	no	—
62	#95×C₄₃	—	2	4	no	—
63	#95×C₄₃	—	4	4	no	—
64	#95×C₄₃	—	4	4	no	—
65	#95×C₄₃	—	4	4	no	—
66	C₂⁴×C₄₃	—	2	1	no	—
67	C₂⁴×C₄₃	—	2	1	no	—
68	C₂⁴×C₄₃	—	2	2	no	—
69	C₂⁴×C₄₃	—	2	2	no	—
70	C₂⁴×C₄₃	—	2	2	no	—
71	C₂⁴×C₄₃	—	2	2	no	—
72	C₂⁴×C₄₃	—	2	2	no	—
73	C₂⁴×C₄₃	—	2	2	no	—
74	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
75	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	—	2	1	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	4	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₃	#41	1	2	yes	—
114	C₂²×C₄×C₄₃	#41	1	4	yes	—
115	C₂²×C₄×C₄₃	#41	1	4	yes	—
116	C₄⋊C₄×C₄₃	—	4	8	no	—
117	C₄⋊C₄×C₄₃	—	4	8	no	—
118	C₄⋊C₄×C₄₃	—	4	8	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₂²⋊C₄×C₄₃	—	2	8	no	—
121	C₂²⋊C₄×C₄₃	—	4	16	no	—
122	C₂²⋊C₄×C₄₃	—	4	4	no	—
123	C₂²⋊C₄×C₄₃	—	4	4	no	—
124	C₄²×C₄₃	—	2	8	no	—
125	C₂³×C₄₃	—	2	2	no	—
126	C₂³×C₄₃	—	2	4	no	—
127	C₂³×C₄₃	—	2	4	no	—
128	C₂³×C₄₃	—	2	4	no	—
129	C₂³×C₄₃	—	4	1	no	—
130	C₂³×C₄₃	—	4	1	no	—
131	C₂³×C₄₃	—	4	1	no	—
132	C₂³×C₄₃	—	4	1	no	—
133	C₂³×C₄₃	—	4	1	no	—
134	C₂³×C₄₃	—	4	1	no	—
135	C₂³×C₄₃	—	4	4	no	—
136	C₂³×C₄₃	—	4	2	no	—
137	C₂³×C₄₃	—	4	4	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	4	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	4	no	—
142	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
144	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
145	C₂³×C₄₃	C₂×#41	1	2	yes	—
146	C₂³×C₄₃	C₂×#41	1	2	yes	—
147	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
148	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
149	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
150	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	8	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	4	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	4	no	—
176	C₂×C₄×C₄₃	—	4	4	no	—
177	C₂×C₄×C₄₃	—	4	4	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	—	4	4	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	4	no	—
185	C₂×C₄×C₄₃	—	4	4	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
189	C₂×C₄×C₄₃	#123	1	4	yes	—
190	C₂×C₄×C₄₃	#124	1	4	yes	—
191	#17066	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	—	4	8	no	—
196	C₂²×C₄₃	—	8	1	no	—
197	C₂²×C₄₃	—	8	1	no	—
198	C₂²×C₄₃	—	8	1	no	—
199	C₂²×C₄₃	—	8	1	no	—
200	C₂²×C₄₃	—	8	4	no	—
201	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
204	C₂²×C₄₃	#535	1	1	yes	characteristic
205	C₂²×C₄₃	#535	1	1	yes	characteristic
206	C₂²×C₄₃	#535	1	1	yes	characteristic
207	C₂²×C₄₃	#536	1	1	yes	characteristic
208	C₂²×C₄₃	#539	1	4	yes	—
209	C₂²×C₄₃	#542	1	2	yes	—
210	C₂²×C₄₃	#542	1	4	yes	—
211	C₂²×C₄₃	#544	1	2	yes	—
212	C₂²×C₄₃	#553	1	2	yes	—
213	C₂²×C₄₃	#553	1	4	yes	—
214	C₂²×C₄₃	#554	1	2	yes	—
215	C₂²×C₄₃	#554	1	2	yes	—
216	C₂²×C₄₃	#555	1	2	yes	—
217	C₂²×C₄₃	#560	1	4	yes	—
218	C₄×C₄₃	—	2	4	no	—
219	C₄×C₄₃	—	2	4	no	—
220	C₄×C₄₃	—	2	4	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	—	8	4	no	—
223	C₄×C₄₃	—	8	1	no	—
224	C₄×C₄₃	—	8	1	no	—
225	C₄×C₄₃	—	8	4	no	—
226	C₂×#388	C₂×C₄₃	1	1	yes	characteristic
227	C₂×#384	C₂×C₄₃	1	1	yes	characteristic, complemented
228	#1442	C₂×C₄₃	1	2	yes	complemented
229	#1442	C₂×C₄₃	1	2	yes	complemented
230	#1441	C₂×C₄₃	1	2	yes	complemented
231	#1439	C₂×C₄₃	1	2	yes	—
232	#1439	C₂×C₄₃	1	2	yes	—
233	#1439	C₂×C₄₃	1	2	yes	—
234	#1434	C₂×C₄₃	1	1	yes	characteristic, complemented
235	C₂×C₄₃	—	8	2	no	—
236	C₂×C₄₃	#2487	1	1	yes	characteristic
237	C₂×C₄₃	#2504	1	1	yes	characteristic
238	C₂×C₄₃	#2563	1	1	yes	characteristic
239	C₂×C₄₃	#2623	1	1	yes	characteristic
240	C₂×C₄₃	#2628	1	1	yes	characteristic
241	C₂×C₄₃	#2640	1	1	yes	characteristic
242	C₂×C₄₃	#2790	1	4	yes	—
243	C₂×C₄₃	#2795	1	4	yes	—
244	C₂×C₄₃	#2818	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
253	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
254	#388	—	2	4	no	—
255	#384	—	2	4	no	—
256	C₂×#95	C₂²×C₄₃	1	2	yes	—
257	C₂×#95	C₂²×C₄₃	1	2	yes	—
258	C₂×#95	C₂²×C₄₃	1	2	yes	—
259	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
261	C₂×#95	C₂²×C₄₃	1	4	yes	—
262	C₂×#95	C₂²×C₄₃	1	4	yes	—
263	C₂×#95	C₂²×C₄₃	1	4	yes	—
264	C₄₃	#17066	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
267	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
270	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	4	4	no	—
280	C₂×C₄⋊C₄	—	4	4	no	—
281	C₂×C₄⋊C₄	—	4	4	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	4	4	no	—
289	C₂×C₂²⋊C₄	—	4	4	no	—
290	C₂×C₂²⋊C₄	—	4	4	no	—
291	C₂×C₂²⋊C₄	Q₈×C₄₃	1	4	yes	—
292	C₂×C₄²	—	2	4	no	—
293	C₂×C₄²	D₄×C₄₃	1	4	yes	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	4	no	—
297	#95	—	2	4	no	—
298	#95	—	2	4	no	—
299	#95	—	4	4	no	—
300	#95	—	4	4	no	—
301	#95	—	4	4	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	—	2	1	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	—	2	2	no	—
308	C₂⁴	—	2	2	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
311	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
347	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
348	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
349	C₂²×C₄	#41×C₄₃	1	2	yes	—
350	C₂²×C₄	#41×C₄₃	1	4	yes	—
351	C₂²×C₄	#41×C₄₃	1	4	yes	—
352	C₄⋊C₄	—	4	8	no	—
353	C₄⋊C₄	—	4	8	no	—
354	C₄⋊C₄	—	4	8	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	4	16	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	8	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	4	no	—
378	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
379	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
380	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
381	C₂³	C₂×#41×C₄₃	1	2	yes	—
382	C₂³	C₂×#41×C₄₃	1	2	yes	—
383	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
384	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
385	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
386	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
425	C₂×C₄	#123×C₄₃	1	4	yes	—
426	C₂×C₄	#124×C₄₃	1	4	yes	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	8	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	4	no	—
435	C₂²	—	8	1	no	—
436	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
437	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
438	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
439	C₂²	C₄₃×#535	1	1	yes	characteristic
440	C₂²	C₄₃×#535	1	1	yes	characteristic
441	C₂²	C₄₃×#535	1	1	yes	characteristic
442	C₂²	C₄₃×#536	1	1	yes	characteristic
443	C₂²	C₄₃×#539	1	4	yes	—
444	C₂²	C₄₃×#542	1	2	yes	—
445	C₂²	C₄₃×#542	1	4	yes	—
446	C₂²	C₄₃×#544	1	2	yes	—
447	C₂²	C₄₃×#553	1	2	yes	—
448	C₂²	C₄₃×#553	1	4	yes	—
449	C₂²	C₄₃×#554	1	2	yes	—
450	C₂²	C₄₃×#554	1	2	yes	—
451	C₂²	C₄₃×#555	1	2	yes	—
452	C₂²	C₄₃×#560	1	4	yes	—
453	C₄	—	2	4	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	4	no	—
460	C₄	—	8	4	no	—
461	C₂	—	8	2	no	—
462	C₂	C₄₃×#2487	1	1	yes	characteristic
463	C₂	C₄₃×#2504	1	1	yes	characteristic
464	C₂	C₄₃×#2563	1	1	yes	characteristic
465	C₂	C₄₃×#2623	1	1	yes	characteristic
466	C₂	C₄₃×#2628	1	1	yes	characteristic
467	C₂	C₄₃×#2640	1	1	yes	characteristic
468	C₂	C₄₃×#2790	1	4	yes	—
469	C₂	C₄₃×#2795	1	4	yes	—
470	C₂	C₄₃×#2818	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#384	C₂	semidirect
3. C₄₃×#1442	C₂	semidirect
4. C₄₃×#1442	C₂	semidirect
5. C₄₃×#1441	C₂	semidirect
9. C₄₃×#1434	C₂	semidirect
191. #17066	C₄₃	direct (N × H)
227. C₂×#384	C₂×C₄₃	semidirect
228. #1442	C₂×C₄₃	semidirect
229. #1442	C₂×C₄₃	semidirect
230. #1441	C₂×C₄₃	semidirect
234. #1434	C₂×C₄₃	semidirect
264. C₄₃	#17066	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×#388	2
C₂×C₄₃×#384	2
C₄₃×#1442	2
C₄₃×#1441	2
C₄₃×#1439	2
C₄₃×#1434	2
#17066	43

Subgroups — C43×#17066 #24937083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17066 #24937083