Subgroups — #25106960

Order 11008.

790 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582959	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582958	C₂	1	1	yes	maximal, characteristic
3	#19137075	C₂	1	1	yes	maximal, characteristic
4	#19135319	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135317	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135316	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135315	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135313	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135312	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135310	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134578	C₂	1	1	yes	maximal, characteristic
12	#19134576	C₂	1	1	yes	maximal, characteristic
13	#19134574	C₂	1	1	yes	maximal, characteristic
14	#19134572	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063282	C₂²	1	1	yes	characteristic
17	C₂×#13063282	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
19	#14582959	—	2	4	no	—
20	#14582958	—	2	4	no	—
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×#13063236	C₂²	1	1	yes	characteristic
35	C₂×#13063235	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	#14582796	C₄	1	1	yes	characteristic
38	#14582796	C₄	1	1	yes	characteristic
39	#14582794	C₄	1	1	yes	characteristic
40	#14582794	C₄	1	1	yes	characteristic
41	#14582773	C₄	1	1	yes	characteristic
42	#14582773	C₄	1	1	yes	characteristic
43	#14582770	C₄	1	1	yes	characteristic
44	#14582770	C₄	1	1	yes	characteristic
45	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
48	#14582654	C₂²	1	1	yes	characteristic
49	#14582654	C₂²	1	1	yes	characteristic
50	#14582653	C₂²	1	1	yes	characteristic
51	#14582653	C₂²	1	1	yes	characteristic
52	#14582653	C₂²	1	1	yes	characteristic
53	#14582653	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	#13063282	—	4	1	no	—
69	#13063282	—	4	1	no	—
70	#13063282	D₄	1	4	yes	—
71	#13063282	Q₈	1	4	yes	—
72	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
91	C₄²×D₄₃	—	4	1	no	—
92	C₄²×D₄₃	—	4	1	no	—
93	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
94	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
95	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
96	Dic₄₃⋊C₈	—	2	2	no	—
97	Dic₄₃⋊C₈	—	2	2	no	—
98	Dic₄₃⋊C₈	—	4	1	no	—
99	Dic₄₃⋊C₈	—	4	1	no	—
100	Dic₄₃⋊C₈	—	4	1	no	—
101	Dic₄₃⋊C₈	—	4	1	no	—
102	(C₂×D₄₃)⋊C₈	—	2	2	no	—
103	(C₂×D₄₃)⋊C₈	—	2	2	no	—
104	(C₂×D₄₃)⋊C₈	—	2	2	no	—
105	(C₂×D₄₃)⋊C₈	—	2	2	no	—
106	#13063236	—	2	2	no	—
107	#13063235	—	2	2	no	—
108	C₈×Dic₄₃	—	2	2	no	—
109	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₄₃	—	2	2	no	—
125	C₄⋊C₈×C₄₃	—	4	1	no	—
126	C₄⋊C₈×C₄₃	—	4	1	no	—
127	C₄×C₈×C₄₃	—	2	2	no	—
128	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
129	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
130	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₄₃	—	2	1	no	—
146	C₂×C₄×D₄₃	—	2	1	no	—
147	C₂×C₄×D₄₃	—	2	1	no	—
148	C₂×C₄×D₄₃	—	2	1	no	—
149	C₂×C₄×D₄₃	—	2	2	no	—
150	C₂×C₄×D₄₃	—	2	2	no	—
151	C₂×C₄×D₄₃	—	4	1	no	—
152	C₂×C₄×D₄₃	—	4	1	no	—
153	C₂×C₄×D₄₃	—	4	1	no	—
154	C₂×C₄×D₄₃	—	4	1	no	—
155	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
156	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
157	C₂×C₈×C₄₃	—	2	1	no	—
158	C₂×C₈×C₄₃	—	2	1	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	—	2	1	no	—
163	C₂×C₈×C₄₃	—	2	1	no	—
164	C₂×C₈×C₄₃	—	2	1	no	—
165	C₂×C₈×C₄₃	—	2	1	no	—
166	C₂×C₈×C₄₃	—	2	1	no	—
167	C₂×C₈×C₄₃	—	2	1	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₄⋊C₄×C₄₃	—	2	2	no	—
170	C₄⋊C₄×C₄₃	—	4	1	no	—
171	C₄²×C₄₃	—	2	1	no	—
172	C₄²×C₄₃	—	2	1	no	—
173	C₄²×C₄₃	—	2	1	no	—
174	C₄²×C₄₃	—	2	1	no	—
175	C₄²×C₄₃	C₂×D₄	1	2	yes	—
176	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
177	(C₂×D₄₃)⋊C₄	—	4	1	no	—
178	(C₂×D₄₃)⋊C₄	—	4	1	no	—
179	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	4	yes	—
180	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	4	yes	—
181	C₄⋊Dic₄₃	—	2	2	no	—
182	C₄⋊Dic₄₃	—	4	1	no	—
183	Dic₄₃⋊C₄	—	2	2	no	—
184	Dic₄₃⋊C₄	—	2	2	no	—
185	Dic₄₃⋊C₄	—	4	1	no	—
186	Dic₄₃⋊C₄	—	4	1	no	—
187	Dic₄₃⋊C₄	—	4	1	no	—
188	Dic₄₃⋊C₄	—	4	1	no	—
189	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
190	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
191	C₄×Dic₄₃	—	2	1	no	—
192	C₄×Dic₄₃	—	2	1	no	—
193	C₄×Dic₄₃	—	2	1	no	—
194	C₄×Dic₄₃	—	2	1	no	—
195	C₄×Dic₄₃	—	4	1	no	—
196	C₄×Dic₄₃	—	4	1	no	—
197	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
198	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
199	C₂×C₄₃⋊C₈	—	2	1	no	—
200	C₂×C₄₃⋊C₈	—	2	1	no	—
201	C₂×C₄₃⋊C₈	—	2	1	no	—
202	C₂×C₄₃⋊C₈	—	2	1	no	—
203	C₂×C₄₃⋊C₈	—	2	1	no	—
204	C₂×C₄₃⋊C₈	—	2	1	no	—
205	C₂×C₄₃⋊C₈	—	2	1	no	—
206	C₂×C₄₃⋊C₈	—	2	1	no	—
207	C₂×C₄₃⋊C₈	—	2	1	no	—
208	C₂×C₄₃⋊C₈	—	2	1	no	—
209	C₂×C₄₃⋊C₈	—	2	1	no	—
210	C₂×C₄₃⋊C₈	—	2	1	no	—
211	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
212	C₂²×D₄₃	—	2	1	no	—
213	C₂²×D₄₃	—	2	1	no	—
214	C₂²×D₄₃	—	2	1	no	—
215	C₂²×D₄₃	—	2	1	no	—
216	C₂²×D₄₃	—	2	1	no	—
217	C₂²×D₄₃	—	2	1	no	—
218	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	1	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	2	1	no	—
233	C₂×C₄×C₄₃	—	2	1	no	—
234	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
235	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
236	C₂×C₄×C₄₃	#131	1	2	yes	—
237	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
239	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
243	C₂×Dic₄₃	—	2	1	no	—
244	C₂×Dic₄₃	—	2	1	no	—
245	C₂×Dic₄₃	—	2	1	no	—
246	C₂×Dic₄₃	—	2	1	no	—
247	C₂×Dic₄₃	—	2	1	no	—
248	C₂×Dic₄₃	—	2	1	no	—
249	C₂×Dic₄₃	—	2	1	no	—
250	C₂×Dic₄₃	—	2	1	no	—
251	C₂×Dic₄₃	—	2	1	no	—
252	C₂×Dic₄₃	—	2	1	no	—
253	C₂×Dic₄₃	—	2	1	no	—
254	C₂×Dic₄₃	—	2	1	no	—
255	C₂×Dic₄₃	—	2	1	no	—
256	C₂×Dic₄₃	—	2	1	no	—
257	C₂×Dic₄₃	—	2	1	no	—
258	C₂×Dic₄₃	—	2	1	no	—
259	C₂×Dic₄₃	—	2	1	no	—
260	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
261	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
262	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
263	C₂×Dic₄₃	#131	1	2	yes	—
264	C₄×D₄₃	—	2	2	no	—
265	C₄×D₄₃	—	2	2	no	—
266	C₄×D₄₃	—	2	2	no	—
267	C₄×D₄₃	—	2	2	no	—
268	C₄×D₄₃	—	4	4	no	—
269	C₄×D₄₃	—	4	4	no	—
270	C₈×C₄₃	—	4	1	no	—
271	C₈×C₄₃	—	4	1	no	—
272	C₈×C₄₃	—	4	1	no	—
273	C₈×C₄₃	—	4	1	no	—
274	C₄₃⋊C₈	—	4	1	no	—
275	C₄₃⋊C₈	—	4	1	no	—
276	C₄₃⋊C₈	—	4	1	no	—
277	C₄₃⋊C₈	—	4	1	no	—
278	#21958	—	43	1	no	maximal, Sylow
279	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×C₄₃	#518	1	1	yes	characteristic
281	C₂²×C₄₃	#519	1	1	yes	characteristic
282	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
283	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
284	C₂²×C₄₃	#568	1	1	yes	characteristic
285	C₂²×C₄₃	#568	1	1	yes	characteristic
286	C₂×D₄₃	—	2	2	no	—
287	C₂×D₄₃	—	2	2	no	—
288	C₂×D₄₃	—	2	2	no	—
289	C₂×D₄₃	—	4	1	no	—
290	C₂×D₄₃	—	4	1	no	—
291	C₂×D₄₃	—	4	1	no	—
292	C₂×D₄₃	—	4	1	no	—
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	2	no	—
295	C₄×C₄₃	—	2	2	no	—
296	C₄×C₄₃	—	4	1	no	—
297	C₄×C₄₃	—	4	1	no	—
298	C₄×C₄₃	—	4	1	no	—
299	C₄×C₄₃	#537	1	1	yes	characteristic
300	C₄×C₄₃	#537	1	1	yes	characteristic
301	C₄×C₄₃	#544	1	1	yes	characteristic
302	C₄×C₄₃	#544	1	1	yes	characteristic
303	Dic₄₃	—	2	2	no	—
304	Dic₄₃	—	2	2	no	—
305	Dic₄₃	—	2	2	no	—
306	Dic₄₃	—	2	2	no	—
307	Dic₄₃	—	4	1	no	—
308	Dic₄₃	—	4	1	no	—
309	Dic₄₃	—	4	1	no	—
310	C₂×#433	—	43	1	no	—
311	C₂×#433	—	43	1	no	—
312	#2296	—	43	1	no	—
313	#1940	—	43	1	no	—
314	#1940	—	43	1	no	—
315	#1940	—	43	1	no	—
316	#1940	—	43	1	no	—
317	#1939	—	43	1	no	—
318	#1939	—	43	1	no	—
319	#1939	—	43	1	no	—
320	#1939	D₄₃	1	1	yes	characteristic, complemented
321	#1798	—	43	1	no	—
322	#1798	—	43	1	no	—
323	#1797	—	43	1	no	—
324	#1797	—	43	1	no	—
325	C₂×C₄₃	#2316	1	1	yes	characteristic
326	C₂×C₄₃	#2906	1	1	yes	characteristic
327	C₂×C₄₃	#2906	1	1	yes	characteristic
328	C₂×C₄₃	#2977	1	1	yes	characteristic
329	C₂×C₄₃	#2978	1	1	yes	characteristic
330	C₂×C₄₃	#2985	1	1	yes	characteristic
331	C₂×C₄₃	#2985	1	1	yes	characteristic
332	D₄₃	—	4	2	no	—
333	C₂×#117	—	43	1	no	—
334	C₂×#117	—	43	1	no	—
335	C₂²×C₄²	—	43	1	no	—
336	#433	—	86	4	no	—
337	#433	—	86	4	no	—
338	C₂×C₄⋊C₈	—	43	1	no	—
339	C₂×C₄⋊C₈	—	43	1	no	—
340	C₂×C₄⋊C₈	—	43	1	no	—
341	C₂×C₄⋊C₈	—	43	1	no	—
342	C₂×C₄⋊C₈	—	43	1	no	—
343	C₂×C₄⋊C₈	—	43	1	no	—
344	C₂×C₄⋊C₈	—	43	1	no	—
345	C₂×C₄⋊C₈	—	43	1	no	—
346	C₂×C₄⋊C₈	—	43	1	no	—
347	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	—	43	1	no	—
351	C₂×C₂²⋊C₈	—	43	1	no	—
352	C₂×C₂²⋊C₈	—	43	1	no	—
353	C₂×C₂²⋊C₈	—	43	1	no	—
354	C₂×#97	—	43	1	no	—
355	C₂×#97	—	43	1	no	—
356	C₂×C₄×C₈	—	43	1	no	—
357	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
358	#389	—	43	1	no	—
359	#389	—	43	1	no	—
360	#389	—	43	1	no	—
361	#389	—	43	1	no	—
362	#385	—	43	1	no	—
363	#385	—	43	1	no	—
364	#385	—	43	1	no	—
365	#385	—	43	1	no	—
366	C₄×C₄⋊C₄	—	43	1	no	—
367	C₄×C₄⋊C₄	—	43	1	no	—
368	C₄×C₄⋊C₄	—	43	1	no	—
369	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
370	#336	—	43	1	no	—
371	#336	—	43	1	no	—
372	#336	—	43	1	no	—
373	#336	—	43	1	no	—
374	#336	—	43	1	no	—
375	#336	—	43	1	no	—
376	#336	C₂×D₄₃	1	1	yes	characteristic
377	#336	C₂×D₄₃	1	1	yes	characteristic
378	C₄₃	#21958	1	1	yes	characteristic, complemented, Sylow
379	C₂³×C₄	—	43	1	no	—
380	C₂³×C₄	—	43	1	no	—
381	C₂³×C₄	—	43	1	no	—
382	C₂²×C₈	—	43	1	no	—
383	C₂²×C₈	—	43	1	no	—
384	C₂²×C₈	—	43	1	no	—
385	C₂²×C₈	—	43	1	no	—
386	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
387	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
388	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
389	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
390	#117	—	43	4	no	—
391	#117	—	43	4	no	—
392	#117	—	172	1	no	—
393	#117	—	172	1	no	—
394	C₂×C₄⋊C₄	—	43	1	no	—
395	C₂×C₄⋊C₄	—	43	1	no	—
396	C₂×C₄⋊C₄	—	43	1	no	—
397	C₂×C₄⋊C₄	—	43	1	no	—
398	C₂×C₄⋊C₄	—	43	1	no	—
399	C₂×C₄⋊C₄	—	43	1	no	—
400	C₂×C₄⋊C₄	—	43	1	no	—
401	C₂×C₄⋊C₄	—	43	1	no	—
402	C₂×C₄⋊C₄	—	43	1	no	—
403	C₂×C₄⋊C₄	—	43	1	no	—
404	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	43	1	no	—
407	C₂×C₂²⋊C₄	—	43	1	no	—
408	C₂×C₂²⋊C₄	—	43	1	no	—
409	C₂×C₂²⋊C₄	—	43	1	no	—
410	C₂×C₄²	—	43	1	no	—
411	C₂×C₄²	—	43	1	no	—
412	C₂×C₄²	—	43	1	no	—
413	C₂×C₄²	—	43	1	no	—
414	C₂×C₄²	—	43	1	no	—
415	C₂×C₄²	—	172	1	no	—
416	C₂×C₄²	—	172	1	no	—
417	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
418	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
419	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	4	1	no	—
422	C₄⋊C₈	—	4	1	no	—
423	C₄⋊C₈	—	86	2	no	—
424	C₄⋊C₈	—	86	2	no	—
425	C₄⋊C₈	—	86	2	no	—
426	C₄⋊C₈	—	172	1	no	—
427	C₄⋊C₈	—	172	1	no	—
428	C₄⋊C₈	—	172	1	no	—
429	C₄⋊C₈	—	172	1	no	—
430	C₄⋊C₈	—	172	1	no	—
431	C₄⋊C₈	—	172	1	no	—
432	C₂²⋊C₈	—	86	2	no	—
433	C₂²⋊C₈	—	86	2	no	—
434	C₂²⋊C₈	—	86	2	no	—
435	C₂²⋊C₈	—	86	2	no	—
436	#97	—	86	2	no	—
437	#97	—	86	2	no	—
438	C₄×C₈	—	2	2	no	—
439	C₄×C₈	—	86	2	no	—
440	#95	—	43	1	no	—
441	#95	—	43	1	no	—
442	#95	—	43	1	no	—
443	#95	—	43	1	no	—
444	#95	—	43	1	no	—
445	#95	—	43	1	no	—
446	#95	C₄×D₄₃	1	1	yes	characteristic
447	#95	C₄×D₄₃	1	1	yes	characteristic
448	C₂⁴	—	43	1	no	—
449	C₂²×C₄	—	43	1	no	—
450	C₂²×C₄	—	43	1	no	—
451	C₂²×C₄	—	43	1	no	—
452	C₂²×C₄	—	43	1	no	—
453	C₂²×C₄	—	43	2	no	—
454	C₂²×C₄	—	43	2	no	—
455	C₂²×C₄	—	43	1	no	—
456	C₂²×C₄	—	43	1	no	—
457	C₂²×C₄	—	43	1	no	—
458	C₂²×C₄	—	86	2	no	—
459	C₂²×C₄	—	86	1	no	—
460	C₂²×C₄	—	86	1	no	—
461	C₂²×C₄	—	86	1	no	—
462	C₂²×C₄	—	86	1	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	172	1	no	—
465	C₂²×C₄	—	172	1	no	—
466	C₂²×C₄	—	172	1	no	—
467	C₂²×C₄	—	172	1	no	—
468	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	86	1	no	—
488	C₂×C₈	—	86	1	no	—
489	C₂×C₈	—	86	1	no	—
490	C₂×C₈	—	86	1	no	—
491	C₂×C₈	—	86	1	no	—
492	C₂×C₈	—	86	1	no	—
493	C₂×C₈	—	86	1	no	—
494	C₂×C₈	—	86	1	no	—
495	C₂×C₈	—	86	1	no	—
496	C₂×C₈	—	86	1	no	—
497	C₂×C₈	—	86	1	no	—
498	C₂×C₈	—	86	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	43	4	no	—
502	C₄⋊C₄	—	43	4	no	—
503	C₄⋊C₄	—	86	2	no	—
504	C₄⋊C₄	—	86	2	no	—
505	C₄⋊C₄	—	86	2	no	—
506	C₄⋊C₄	—	172	1	no	—
507	C₄⋊C₄	—	172	1	no	—
508	C₄⋊C₄	—	172	1	no	—
509	C₄⋊C₄	—	172	1	no	—
510	C₄⋊C₄	—	172	1	no	—
511	C₂²⋊C₄	—	43	4	no	—
512	C₂²⋊C₄	—	43	4	no	—
513	C₂²⋊C₄	—	172	1	no	—
514	C₂²⋊C₄	—	172	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	43	2	no	—
520	C₄²	—	43	2	no	—
521	C₄²	—	86	1	no	—
522	C₄²	—	86	1	no	—
523	C₄²	—	86	1	no	—
524	C₄²	—	86	1	no	—
525	C₄²	—	172	1	no	—
526	C₄²	—	172	1	no	—
527	C₄²	D₄×D₄₃	1	2	yes	—
528	C₄²	Q₈×D₄₃	1	2	yes	—
529	C₂³	—	43	2	no	—
530	C₂³	—	86	1	no	—
531	C₂³	—	86	1	no	—
532	C₂³	—	86	1	no	—
533	C₂³	—	86	1	no	—
534	C₂³	—	86	1	no	—
535	C₂³	—	86	1	no	—
536	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	43	2	no	—
553	C₂×C₄	—	43	2	no	—
554	C₂×C₄	—	43	2	no	—
555	C₂×C₄	—	43	2	no	—
556	C₂×C₄	—	86	1	no	—
557	C₂×C₄	—	86	1	no	—
558	C₂×C₄	—	86	1	no	—
559	C₂×C₄	—	86	1	no	—
560	C₂×C₄	—	86	1	no	—
561	C₂×C₄	—	86	1	no	—
562	C₂×C₄	—	86	1	no	—
563	C₂×C₄	—	86	1	no	—
564	C₂×C₄	—	86	2	no	—
565	C₂×C₄	—	86	2	no	—
566	C₂×C₄	—	86	2	no	—
567	C₂×C₄	—	86	2	no	—
568	C₂×C₄	—	86	1	no	—
569	C₂×C₄	—	86	1	no	—
570	C₂×C₄	—	86	1	no	—
571	C₂×C₄	—	86	1	no	—
572	C₂×C₄	—	86	1	no	—
573	C₂×C₄	—	86	1	no	—
574	C₂×C₄	—	86	1	no	—
575	C₂×C₄	—	86	1	no	—
576	C₂×C₄	—	86	1	no	—
577	C₂×C₄	—	172	4	no	—
578	C₂×C₄	—	172	4	no	—
579	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
580	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
581	C₂×C₄	#13063331	1	2	yes	—
582	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
583	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
584	C₂×C₄	#13063370	1	1	yes	characteristic
585	C₂×C₄	#13063371	1	1	yes	characteristic
586	C₂×C₄	#13063372	1	1	yes	characteristic
587	C₂×C₄	#13063373	1	1	yes	characteristic
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	172	1	no	—
593	C₈	—	172	1	no	—
594	C₈	—	172	1	no	—
595	C₈	—	172	1	no	—
596	C₂²	—	86	2	no	—
597	C₂²	—	86	2	no	—
598	C₂²	—	86	2	no	—
599	C₂²	—	172	1	no	—
600	C₂²	—	172	1	no	—
601	C₂²	—	172	1	no	—
602	C₂²	—	172	1	no	—
603	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
604	C₂²	#14583371	1	1	yes	characteristic
605	C₂²	#14583375	1	1	yes	characteristic
606	C₂²	#131×D₄₃	1	1	yes	characteristic
607	C₂²	C₂×#13063331	1	1	yes	characteristic
608	C₂²	#14583664	1	1	yes	characteristic
609	C₂²	#14583665	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	86	2	no	—
617	C₄	—	86	2	no	—
618	C₄	—	86	2	no	—
619	C₄	—	86	2	no	—
620	C₄	—	172	1	no	—
621	C₄	—	172	1	no	—
622	C₄	—	172	1	no	—
623	C₄	#14583478	1	1	yes	characteristic
624	C₄	#14583479	1	1	yes	characteristic
625	C₄	#14583526	1	1	yes	characteristic
626	C₄	#14583529	1	1	yes	characteristic
627	C₂	—	172	2	no	—
628	C₂	#19137210	1	1	yes	characteristic
629	C₂	#19143160	1	1	yes	characteristic
630	C₂	#19143162	1	1	yes	characteristic
631	C₂	#19143648	1	1	yes	characteristic
632	C₂	#19143652	1	1	yes	characteristic
633	C₂	#19143686	1	1	yes	characteristic
634	C₂	#19143688	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1939	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1939	D₄₃
hypocenter	C₄₃	#21958
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
4. #19135319	C₂	semidirect
5. #19135317	C₂	semidirect
6. #19135316	C₂	semidirect
7. #19135315	C₂	semidirect
8. #19135313	C₂	semidirect
9. #19135312	C₂	semidirect
10. #19135310	C₂	semidirect
15. C₄₃×#1939	C₂	semidirect
320. #1939	D₄₃	semidirect
378. C₄₃	#21958	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582959	2
C₂×#14582958	2
#19137075	2
#19135319	2
#19135317	2
#19135316	2
#19135315	2
#19135313	2
#19135312	2
#19135310	2
#19134578	2
#19134576	2
#19134574	2
#19134572	2
C₄₃×#1939	2
#21958	43