Subgroups — #25100796

Order 11008.

860 conjugacy classes of subgroups.

The subgroup lattice has 680 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, complemented
2	C₂×#14582955	C₂	1	1	yes	maximal, characteristic, complemented
3	#19137036	C₂	1	1	yes	maximal, characteristic
4	#19135393	C₂	1	1	yes	maximal, characteristic
5	#19135388	C₂	1	1	yes	maximal, characteristic
6	#19135314	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135209	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135209	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135200	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135200	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134454	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134360	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134352	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₁₇₂	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	#14582955	—	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×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₃)⋊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×#13063235	C₂²	1	1	yes	characteristic
33	C₂×#13063235	C₂²	1	1	yes	characteristic
34	C₂×#13063235	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
39	#14582789	C₄	1	1	yes	characteristic
40	#14582789	C₄	1	1	yes	characteristic
41	#14582782	C₄	1	1	yes	characteristic
42	#14582782	C₄	1	1	yes	characteristic
43	#14582777	C₄	1	1	yes	characteristic
44	#14582777	C₄	1	1	yes	characteristic
45	#14582770	C₄	1	1	yes	characteristic
46	#14582770	C₄	1	1	yes	characteristic
47	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
49	#14582745	C₂²	1	1	yes	characteristic
50	#14582654	C₂²	1	1	yes	characteristic
51	#14582654	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×#97×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×D₁₇₂	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₄×D₁₇₂	—	2	2	no	—
71	C₄×D₁₇₂	—	2	2	no	—
72	#13063282	—	2	2	no	—
73	#13063282	—	2	2	no	—
74	C₂×C₄⋊Dic₄₃	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×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₃)⋊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×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
89	C₄²×D₄₃	—	2	2	no	—
90	C₄²×D₄₃	—	2	2	no	—
91	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
92	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
93	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
94	(C₂×D₄₃)⋊C₈	—	2	2	no	—
95	(C₂×D₄₃)⋊C₈	—	2	2	no	—
96	(C₂×D₄₃)⋊C₈	—	2	2	no	—
97	(C₂×D₄₃)⋊C₈	—	2	2	no	—
98	(C₂×D₄₃)⋊C₈	—	2	2	no	—
99	(C₂×D₄₃)⋊C₈	—	2	2	no	—
100	(C₂×D₄₃)⋊C₈	—	2	2	no	—
101	(C₂×D₄₃)⋊C₈	—	2	2	no	—
102	#13063235	—	2	2	no	—
103	#13063235	—	2	2	no	—
104	#13063235	D₄	1	4	yes	complemented
105	C₄×C₄₃⋊C₈	—	2	2	no	—
106	C₈×Dic₄₃	—	2	2	no	—
107	C₈×Dic₄₃	—	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	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₄₃	—	2	2	no	—
127	C₄⋊C₈×C₄₃	—	2	2	no	—
128	C₄⋊C₈×C₄₃	—	2	2	no	—
129	#97×C₄₃	—	2	2	no	—
130	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
131	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
132	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂³×D₄₃	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	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂⁴	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	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	2	no	—
149	C₂×D₁₇₂	—	4	1	no	—
150	C₂×C₄×D₄₃	—	2	2	no	—
151	C₂×C₄×D₄₃	—	2	1	no	—
152	C₂×C₄×D₄₃	—	2	1	no	—
153	C₂×C₄×D₄₃	—	2	1	no	—
154	C₂×C₄×D₄₃	—	2	1	no	—
155	C₂×C₄×D₄₃	—	2	1	no	—
156	C₂×C₄×D₄₃	—	2	1	no	—
157	C₂×C₄×D₄₃	—	2	1	no	—
158	C₂×C₄×D₄₃	—	2	1	no	—
159	C₂×C₄×D₄₃	—	2	1	no	—
160	C₂×C₄×D₄₃	—	2	1	no	—
161	C₂×C₄×D₄₃	—	2	1	no	—
162	C₂×C₄×D₄₃	—	2	1	no	—
163	C₂×C₄×D₄₃	—	2	2	no	—
164	C₂×C₄×D₄₃	—	2	2	no	—
165	C₂×C₄×D₄₃	—	2	2	no	—
166	C₂×C₄×D₄₃	—	4	1	no	—
167	C₂×C₄×D₄₃	—	4	1	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₂×C₈×C₄₃	—	2	1	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	1	no	—
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	2	1	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	1	no	—
178	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₄₃	#41	1	2	yes	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	4	1	no	—
182	C₄²×C₄₃	—	2	1	no	—
183	C₄²×C₄₃	—	2	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₄²×C₄₃	—	2	1	no	—
186	C₄²×C₄₃	#41	1	2	yes	—
187	C₄²×C₄₃	#41	1	2	yes	—
188	(C₂×D₄₃)⋊C₄	—	2	2	no	—
189	(C₂×D₄₃)⋊C₄	—	2	2	no	—
190	(C₂×D₄₃)⋊C₄	—	2	2	no	—
191	(C₂×D₄₃)⋊C₄	—	2	2	no	—
192	(C₂×D₄₃)⋊C₄	—	2	2	no	—
193	(C₂×D₄₃)⋊C₄	—	2	2	no	—
194	(C₂×D₄₃)⋊C₄	—	4	1	no	—
195	(C₂×D₄₃)⋊C₄	—	4	1	no	—
196	C₄⋊Dic₄₃	—	2	2	no	—
197	Dic₄₃⋊C₄	—	2	2	no	—
198	Dic₄₃⋊C₄	—	2	2	no	—
199	C₄×Dic₄₃	—	2	1	no	—
200	C₄×Dic₄₃	—	2	1	no	—
201	C₄×Dic₄₃	—	2	2	no	—
202	C₄×Dic₄₃	—	2	2	no	—
203	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
204	C₄×Dic₄₃	#41	1	2	yes	—
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	C₂×C₄₃⋊C₈	—	2	1	no	—
212	C₂×C₄₃⋊C₈	—	2	1	no	—
213	C₂×C₄₃⋊C₈	—	2	1	no	—
214	C₂×C₄₃⋊C₈	—	2	1	no	—
215	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
216	C₂×C₄₃⋊C₈	#41	1	2	yes	—
217	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
218	C₂²×D₄₃	—	2	1	no	—
219	C₂²×D₄₃	—	2	1	no	—
220	C₂²×D₄₃	—	2	1	no	—
221	C₂²×D₄₃	—	2	1	no	—
222	C₂²×D₄₃	—	2	1	no	—
223	C₂²×D₄₃	—	2	1	no	—
224	C₂²×D₄₃	—	2	1	no	—
225	C₂²×D₄₃	—	2	1	no	—
226	C₂²×D₄₃	—	2	1	no	—
227	C₂²×D₄₃	—	2	1	no	—
228	C₂²×D₄₃	—	2	1	no	—
229	C₂²×D₄₃	—	2	1	no	—
230	C₂²×D₄₃	—	2	1	no	—
231	C₂²×D₄₃	#131	1	2	yes	—
232	C₂×C₄×C₄₃	—	2	1	no	—
233	C₂×C₄×C₄₃	—	2	1	no	—
234	C₂×C₄×C₄₃	—	2	1	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	1	no	—
238	C₂×C₄×C₄₃	—	2	1	no	—
239	C₂×C₄×C₄₃	—	2	1	no	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	1	no	—
245	C₂×C₄×C₄₃	—	2	1	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	#117	1	2	yes	—
248	C₂×C₄×C₄₃	#117	1	2	yes	—
249	C₂×C₄×C₄₃	#131	1	2	yes	—
250	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
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	—	2	1	no	—
261	C₂×Dic₄₃	—	2	1	no	—
262	C₂×Dic₄₃	—	2	1	no	—
263	C₂×Dic₄₃	—	2	1	no	—
264	C₂×Dic₄₃	—	2	1	no	—
265	C₂×Dic₄₃	—	2	1	no	—
266	C₂×Dic₄₃	—	2	1	no	—
267	C₂×Dic₄₃	—	2	1	no	—
268	C₂×Dic₄₃	—	2	1	no	—
269	C₂×Dic₄₃	—	2	1	no	—
270	C₂×Dic₄₃	—	2	1	no	—
271	C₂×Dic₄₃	—	2	1	no	—
272	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
273	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
274	D₁₇₂	—	4	4	no	—
275	C₄×D₄₃	—	4	4	no	—
276	C₄×D₄₃	—	4	4	no	—
277	C₄×D₄₃	—	4	1	no	—
278	C₄×D₄₃	—	4	1	no	—
279	C₄×D₄₃	—	4	1	no	—
280	C₄×D₄₃	—	4	1	no	—
281	C₄×D₄₃	—	4	1	no	—
282	C₄×D₄₃	—	4	1	no	—
283	C₄×D₄₃	—	4	1	no	—
284	C₄×D₄₃	—	4	1	no	—
285	C₈×C₄₃	—	2	2	no	—
286	C₈×C₄₃	—	2	2	no	—
287	C₈×C₄₃	—	4	1	no	—
288	C₈×C₄₃	—	4	1	no	—
289	C₄₃⋊C₈	—	2	2	no	—
290	C₄₃⋊C₈	—	2	2	no	—
291	C₄₃⋊C₈	—	4	1	no	—
292	C₄₃⋊C₈	—	4	1	no	—
293	#21273	—	43	1	no	maximal, Sylow
294	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
295	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
297	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
298	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
299	C₂²×C₄₃	#568	1	1	yes	characteristic
300	C₂²×C₄₃	#568	1	1	yes	characteristic
301	C₂×D₄₃	—	2	2	no	—
302	C₂×D₄₃	—	2	2	no	—
303	C₂×D₄₃	—	2	2	no	—
304	C₂×D₄₃	—	4	1	no	—
305	C₂×D₄₃	—	4	1	no	—
306	C₂×D₄₃	—	4	1	no	—
307	C₂×D₄₃	—	4	1	no	—
308	C₂×D₄₃	—	4	1	no	—
309	C₂×D₄₃	—	4	1	no	—
310	C₂×D₄₃	—	4	1	no	—
311	C₂×D₄₃	—	4	1	no	—
312	C₂×D₄₃	—	4	1	no	—
313	C₂×D₄₃	—	4	1	no	—
314	C₂×D₄₃	—	4	1	no	—
315	C₄×C₄₃	—	2	2	no	—
316	C₄×C₄₃	—	2	2	no	—
317	C₄×C₄₃	—	2	2	no	—
318	C₄×C₄₃	—	4	1	no	—
319	C₄×C₄₃	—	4	1	no	—
320	C₄×C₄₃	—	4	1	no	—
321	C₄×C₄₃	#529	1	1	yes	characteristic
322	C₄×C₄₃	#529	1	1	yes	characteristic
323	C₄×C₄₃	#532	1	1	yes	characteristic
324	C₄×C₄₃	#532	1	1	yes	characteristic
325	Dic₄₃	—	2	2	no	—
326	Dic₄₃	—	2	2	no	—
327	Dic₄₃	—	4	1	no	—
328	Dic₄₃	—	4	1	no	—
329	Dic₄₃	—	4	1	no	—
330	Dic₄₃	—	4	1	no	—
331	C₂×#433	—	43	1	no	—
332	C₂×#432	—	43	1	no	—
333	#2290	—	43	1	no	—
334	#1955	—	43	1	no	—
335	#1954	—	43	1	no	—
336	#1940	D₄₃	1	1	yes	characteristic, complemented
337	#1939	—	43	1	no	—
338	#1924	—	43	1	no	—
339	#1924	—	43	1	no	—
340	#1923	—	43	1	no	—
341	#1923	—	43	1	no	—
342	#1768	—	43	1	no	—
343	#1750	—	43	1	no	—
344	C₄×C₂²⋊C₈	—	43	1	no	—
345	#1726	—	43	1	no	—
346	C₂×C₄₃	#2293	1	1	yes	characteristic
347	C₂×C₄₃	#2924	1	1	yes	characteristic
348	C₂×C₄₃	#2925	1	1	yes	characteristic
349	C₂×C₄₃	#2933	1	1	yes	characteristic
350	C₂×C₄₃	#2933	1	1	yes	characteristic
351	C₂×C₄₃	#2966	1	1	yes	characteristic
352	C₂×C₄₃	#2967	1	1	yes	characteristic
353	D₄₃	—	4	2	no	—
354	D₄₃	—	8	1	no	—
355	C₂×C₄×D₄	—	43	1	no	—
356	C₂×#117	—	43	1	no	—
357	C₂²×C₄²	—	43	1	no	—
358	#433	—	86	4	no	—
359	#432	—	86	4	no	—
360	C₂×C₄⋊C₈	—	43	1	no	—
361	C₂×C₄⋊C₈	—	43	1	no	—
362	C₂×C₄⋊C₈	—	43	1	no	—
363	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
365	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	—	43	1	no	—
367	C₂×C₂²⋊C₈	—	43	1	no	—
368	C₂×C₂²⋊C₈	—	43	1	no	—
369	C₂×C₂²⋊C₈	—	43	1	no	—
370	C₂×C₂²⋊C₈	—	43	1	no	—
371	C₂×C₂²⋊C₈	—	43	1	no	—
372	C₂×C₂²⋊C₈	—	43	1	no	—
373	C₂×C₂²⋊C₈	—	43	1	no	—
374	C₂×#97	—	43	1	no	—
375	C₂×#97	—	43	1	no	—
376	C₂×#97	—	43	1	no	—
377	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
378	C₂×C₄×C₈	—	43	1	no	—
379	C₂×C₄×C₈	—	43	1	no	—
380	C₂×C₄×C₈	—	43	1	no	—
381	C₂×C₄×C₈	—	43	1	no	—
382	#388	—	43	1	no	—
383	#388	—	43	1	no	—
384	#387	—	43	1	no	—
385	#387	—	43	1	no	—
386	#386	—	43	1	no	—
387	#386	—	43	1	no	—
388	#385	—	43	1	no	—
389	#385	—	43	1	no	—
390	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
391	C₄×C₂²⋊C₄	—	43	1	no	—
392	C₄×C₂²⋊C₄	—	43	1	no	—
393	#376	—	43	1	no	—
394	#336	—	43	1	no	—
395	#336	—	43	1	no	—
396	#336	—	43	1	no	—
397	#336	—	43	1	no	—
398	#336	C₂×D₄₃	1	1	yes	characteristic
399	#336	C₂×D₄₃	1	1	yes	characteristic
400	C₄₃	#21273	1	1	yes	characteristic, complemented, Sylow
401	C₂²×D₄	—	43	1	no	—
402	C₂³×C₄	—	43	1	no	—
403	C₂³×C₄	—	43	1	no	—
404	C₂³×C₄	—	43	1	no	—
405	C₂³×C₄	—	43	1	no	—
406	C₂²×C₈	—	43	1	no	—
407	C₂²×C₈	—	43	1	no	—
408	C₂²×C₈	—	43	1	no	—
409	C₂²×C₈	—	43	1	no	—
410	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
411	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
412	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
413	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
414	C₄×D₄	—	86	2	no	—
415	C₄×D₄	—	86	2	no	—
416	#117	—	86	2	no	—
417	#117	—	86	2	no	—
418	C₂×C₄⋊C₄	—	43	1	no	—
419	C₂×C₄⋊C₄	—	43	1	no	—
420	C₂×C₄⋊C₄	—	43	1	no	—
421	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	43	1	no	—
424	C₂×C₂²⋊C₄	—	43	1	no	—
425	C₂×C₂²⋊C₄	—	43	1	no	—
426	C₂×C₂²⋊C₄	—	43	1	no	—
427	C₂×C₂²⋊C₄	—	43	1	no	—
428	C₂×C₂²⋊C₄	—	43	1	no	—
429	C₂×C₂²⋊C₄	—	43	1	no	—
430	C₂×C₂²⋊C₄	—	43	1	no	—
431	C₂×C₄²	—	43	1	no	—
432	C₂×C₄²	—	43	1	no	—
433	C₂×C₄²	—	43	1	no	—
434	C₂×C₄²	—	43	1	no	—
435	C₂×C₄²	—	86	2	no	—
436	C₂×C₄²	—	86	2	no	—
437	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	86	2	no	—
444	C₄⋊C₈	—	86	2	no	—
445	C₄⋊C₈	—	86	2	no	—
446	C₂²⋊C₈	—	86	2	no	—
447	C₂²⋊C₈	—	86	2	no	—
448	C₂²⋊C₈	—	86	2	no	—
449	C₂²⋊C₈	—	86	2	no	—
450	C₂²⋊C₈	—	86	2	no	—
451	C₂²⋊C₈	—	86	2	no	—
452	C₂²⋊C₈	—	86	2	no	—
453	C₂²⋊C₈	—	86	2	no	—
454	#97	—	2	2	no	—
455	#97	—	43	4	no	—
456	#97	—	86	2	no	—
457	#97	—	86	2	no	—
458	C₄×C₈	—	86	2	no	—
459	C₄×C₈	—	86	2	no	—
460	C₄×C₈	—	86	2	no	—
461	C₄×C₈	—	86	2	no	—
462	#95	—	43	1	no	—
463	#95	—	43	1	no	—
464	#95	—	43	1	no	—
465	#95	—	43	1	no	—
466	#95	—	43	1	no	—
467	#95	—	43	1	no	—
468	#95	—	43	1	no	—
469	#95	—	43	1	no	—
470	#95	C₄×D₄₃	1	1	yes	characteristic
471	#95	C₄×D₄₃	1	1	yes	characteristic
472	C₂⁴	—	43	1	no	—
473	C₂⁴	—	43	1	no	—
474	C₂×D₄	—	86	2	no	—
475	C₂×D₄	—	86	2	no	—
476	C₂×D₄	—	172	1	no	—
477	C₂²×C₄	—	43	1	no	—
478	C₂²×C₄	—	43	1	no	—
479	C₂²×C₄	—	43	1	no	—
480	C₂²×C₄	—	43	1	no	—
481	C₂²×C₄	—	43	1	no	—
482	C₂²×C₄	—	43	1	no	—
483	C₂²×C₄	—	86	2	no	—
484	C₂²×C₄	—	86	2	no	—
485	C₂²×C₄	—	86	2	no	—
486	C₂²×C₄	—	86	2	no	—
487	C₂²×C₄	—	86	1	no	—
488	C₂²×C₄	—	86	1	no	—
489	C₂²×C₄	—	86	1	no	—
490	C₂²×C₄	—	86	1	no	—
491	C₂²×C₄	—	86	1	no	—
492	C₂²×C₄	—	86	1	no	—
493	C₂²×C₄	—	86	1	no	—
494	C₂²×C₄	—	86	1	no	—
495	C₂²×C₄	—	86	1	no	—
496	C₂²×C₄	—	86	1	no	—
497	C₂²×C₄	—	86	1	no	—
498	C₂²×C₄	—	86	1	no	—
499	C₂²×C₄	—	172	1	no	—
500	C₂²×C₄	—	172	1	no	—
501	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	43	2	no	—
519	C₂×C₈	—	43	2	no	—
520	C₂×C₈	—	86	1	no	—
521	C₂×C₈	—	86	1	no	—
522	C₂×C₈	—	86	1	no	—
523	C₂×C₈	—	86	1	no	—
524	C₂×C₈	—	86	1	no	—
525	C₂×C₈	—	86	1	no	—
526	C₂×C₈	—	86	1	no	—
527	C₂×C₈	—	86	1	no	—
528	C₂×C₈	—	86	1	no	—
529	C₂×C₈	—	86	1	no	—
530	C₂×C₈	D₄×D₄₃	1	2	yes	—
531	C₂×C₈	#10621902	1	2	yes	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	4	1	no	—
534	C₄⋊C₄	—	86	2	no	—
535	C₄⋊C₄	—	86	2	no	—
536	C₄⋊C₄	—	86	2	no	—
537	C₂²⋊C₄	—	86	2	no	—
538	C₂²⋊C₄	—	86	2	no	—
539	C₂²⋊C₄	—	86	2	no	—
540	C₂²⋊C₄	—	86	2	no	—
541	C₂²⋊C₄	—	86	2	no	—
542	C₂²⋊C₄	—	86	2	no	—
543	C₂²⋊C₄	—	172	1	no	—
544	C₂²⋊C₄	—	172	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	43	2	no	—
550	C₄²	—	43	2	no	—
551	C₄²	—	86	2	no	—
552	C₄²	—	86	2	no	—
553	C₄²	—	86	1	no	—
554	C₄²	—	86	1	no	—
555	C₄²	#10621900	1	2	yes	—
556	C₄²	#10621902	1	2	yes	—
557	C₂³	—	43	2	no	—
558	C₂³	—	86	1	no	—
559	C₂³	—	86	1	no	—
560	C₂³	—	86	1	no	—
561	C₂³	—	86	1	no	—
562	C₂³	—	86	1	no	—
563	C₂³	—	86	1	no	—
564	C₂³	—	86	1	no	—
565	C₂³	—	86	1	no	—
566	C₂³	—	86	1	no	—
567	C₂³	—	86	1	no	—
568	C₂³	—	86	1	no	—
569	C₂³	—	86	1	no	—
570	C₂³	—	86	1	no	—
571	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
572	D₄	—	172	4	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	43	2	no	—
589	C₂×C₄	—	43	2	no	—
590	C₂×C₄	—	86	1	no	—
591	C₂×C₄	—	86	1	no	—
592	C₂×C₄	—	86	1	no	—
593	C₂×C₄	—	86	1	no	—
594	C₂×C₄	—	86	1	no	—
595	C₂×C₄	—	86	1	no	—
596	C₂×C₄	—	86	1	no	—
597	C₂×C₄	—	86	1	no	—
598	C₂×C₄	—	86	1	no	—
599	C₂×C₄	—	86	1	no	—
600	C₂×C₄	—	86	1	no	—
601	C₂×C₄	—	86	1	no	—
602	C₂×C₄	—	86	1	no	—
603	C₂×C₄	—	86	1	no	—
604	C₂×C₄	—	86	1	no	—
605	C₂×C₄	—	86	1	no	—
606	C₂×C₄	—	172	4	no	—
607	C₂×C₄	—	172	4	no	—
608	C₂×C₄	—	172	1	no	—
609	C₂×C₄	—	172	1	no	—
610	C₂×C₄	—	172	1	no	—
611	C₂×C₄	—	172	1	no	—
612	C₂×C₄	—	172	1	no	—
613	C₂×C₄	—	172	1	no	—
614	C₂×C₄	—	172	1	no	—
615	C₂×C₄	—	172	1	no	—
616	C₂×C₄	#13063283	1	2	yes	—
617	C₂×C₄	#13063283	1	2	yes	—
618	C₂×C₄	#13063333	1	2	yes	—
619	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
620	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
621	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
622	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
623	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
624	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₈	—	86	2	no	—
630	C₈	—	86	2	no	—
631	C₈	—	172	1	no	—
632	C₈	—	172	1	no	—
633	C₂²	—	86	2	no	—
634	C₂²	—	86	2	no	—
635	C₂²	—	86	2	no	—
636	C₂²	—	172	1	no	—
637	C₂²	—	172	1	no	—
638	C₂²	—	172	1	no	—
639	C₂²	—	172	1	no	—
640	C₂²	—	172	1	no	—
641	C₂²	—	172	1	no	—
642	C₂²	—	172	1	no	—
643	C₂²	—	172	1	no	—
644	C₂²	—	172	1	no	—
645	C₂²	—	172	1	no	—
646	C₂²	—	172	1	no	—
647	C₂²	C₂×#13063283	1	1	yes	characteristic
648	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
649	C₂²	C₄×#10621902	1	1	yes	characteristic
650	C₂²	#131×D₄₃	1	1	yes	characteristic
651	C₂²	C₂×#13063333	1	1	yes	characteristic
652	C₂²	#14583664	1	1	yes	characteristic
653	C₂²	#14583665	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	86	2	no	—
661	C₄	—	86	2	no	—
662	C₄	—	172	1	no	—
663	C₄	—	172	1	no	—
664	C₄	—	172	1	no	—
665	C₄	—	172	1	no	—
666	C₄	#14583434	1	1	yes	characteristic
667	C₄	#14583435	1	1	yes	characteristic
668	C₄	#14583444	1	1	yes	characteristic
669	C₄	#14583450	1	1	yes	characteristic
670	C₂	—	344	1	no	—
671	C₂	—	172	2	no	—
672	C₂	#19137053	1	1	yes	characteristic
673	C₂	#19143252	1	1	yes	characteristic
674	C₂	#19143263	1	1	yes	characteristic
675	C₂	#19143318	1	1	yes	characteristic
676	C₂	#19143321	1	1	yes	characteristic
677	C₂	#19143569	1	1	yes	characteristic
678	C₂	#19143579	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1940	C₂
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1940	D₄₃
hypocenter	C₄₃	#21273
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1940

Complements

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

N	H ≅ G/N	type
1. C₂×#14582959	C₂	semidirect
2. C₂×#14582955	C₂	semidirect
6. #19135314	C₂	semidirect
7. #19135209	C₂	semidirect
8. #19135209	C₂	semidirect
9. #19135200	C₂	semidirect
10. #19135200	C₂	semidirect
11. #19134454	C₂	semidirect
12. #19134360	C₂	semidirect
13. #19134352	C₂	semidirect
14. #19134283	C₂	semidirect
15. C₄₃×#1940	C₂	semidirect
104. #13063235	D₄	semidirect
336. #1940	D₄₃	semidirect
400. C₄₃	#21273	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×#14582955	2
#19137036	2
#19135393	2
#19135388	2
#19135314	2
#19135209	2
#19135200	2
#19134454	2
#19134360	2
#19134352	2
#19134283	2
C₄₃×#1940	2
#21273	43