Subgroups — #25107250

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137040	C₂	1	1	yes	maximal, characteristic
2	#19135204	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135198	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135153	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135151	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134888	C₂	1	1	yes	maximal, characteristic
7	#19134773	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134772	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134739	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134713	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134664	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134577	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14582653	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1869	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×#13063284	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
28	#14582792	C₄	1	1	yes	characteristic
29	#14582792	C₄	1	1	yes	characteristic
30	#14582785	C₄	1	1	yes	characteristic
31	#14582785	C₄	1	1	yes	characteristic
32	#14582779	C₄	1	1	yes	characteristic
33	#14582779	C₄	1	1	yes	characteristic
34	#14582774	C₄	1	1	yes	characteristic
35	#14582774	C₄	1	1	yes	characteristic
36	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
39	#14582745	C₂²	1	1	yes	characteristic
40	#14582654	C₂²	1	1	yes	characteristic
41	#14582654	C₂²	1	1	yes	characteristic
42	#14582653	C₂²	1	1	yes	characteristic
43	#14582653	C₂²	1	1	yes	characteristic
44	#14582653	C₂²	1	1	yes	characteristic
45	#14582653	C₂²	1	1	yes	characteristic
46	#14582653	C₂²	1	1	yes	characteristic
47	#14582653	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	#14582653	C₂²	1	1	yes	characteristic
51	#14582653	C₂²	1	1	yes	characteristic
52	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#336	C₂²	1	1	yes	characteristic
58	C₄₃×#336	C₂²	1	1	yes	characteristic
59	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	—	2	2	no	—
62	C₂²×C₄₃⋊C₈	—	4	1	no	—
63	C₂²×C₄₃⋊C₈	—	4	1	no	—
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	#13063284	—	4	1	no	—
69	#13063284	—	4	1	no	—
70	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₄₃	—	4	1	no	—
81	C₂×C₄×Dic₄₃	—	4	1	no	—
82	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
88	Dic₄₃⋊C₈	—	4	1	no	—
89	Dic₄₃⋊C₈	—	4	1	no	—
90	Dic₄₃⋊C₈	—	4	1	no	—
91	Dic₄₃⋊C₈	—	4	1	no	—
92	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
94	C₂²⋊(C₄₃⋊C₈)	—	4	1	no	—
95	C₈×Dic₄₃	—	4	1	no	—
96	C₈×Dic₄₃	—	4	1	no	—
97	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
98	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
99	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
100	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
101	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
102	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
103	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
104	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
105	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₃	—	2	2	no	—
111	C₂²×C₈×C₄₃	—	4	1	no	—
112	C₂²×C₈×C₄₃	—	4	1	no	—
113	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₄₃	—	2	2	no	—
118	C₄×D₄×C₄₃	—	2	2	no	—
119	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²⋊C₈×C₄₃	—	2	2	no	—
124	C₂²⋊C₈×C₄₃	—	4	1	no	—
125	C₂²⋊C₈×C₄₃	—	4	1	no	—
126	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	#41	1	2	yes	—
146	C₂²×C₄×C₄₃	#41	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₂²×Dic₄₃	—	2	2	no	—
149	C₂²×Dic₄₃	—	2	2	no	—
150	C₂²×Dic₄₃	—	2	2	no	—
151	C₂²×Dic₄₃	—	2	2	no	—
152	C₂²×Dic₄₃	—	4	1	no	—
153	C₂²×Dic₄₃	—	4	1	no	—
154	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
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	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	—	4	4	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₂²⋊C₄×C₄₃	—	2	2	no	—
177	C₂²⋊C₄×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	—	2	1	no	—
179	C₄²×C₄₃	—	2	1	no	—
180	C₂²⋊Dic₄₃	—	2	2	no	—
181	C₂²⋊Dic₄₃	—	2	2	no	—
182	C₂²⋊Dic₄₃	—	2	2	no	—
183	C₂²⋊Dic₄₃	—	2	2	no	—
184	C₂²⋊Dic₄₃	—	4	1	no	—
185	C₂²⋊Dic₄₃	—	4	1	no	—
186	C₄⋊Dic₄₃	—	2	2	no	—
187	C₄⋊Dic₄₃	—	2	2	no	—
188	C₄⋊Dic₄₃	—	4	1	no	—
189	C₄⋊Dic₄₃	—	4	1	no	—
190	C₄×Dic₄₃	—	2	1	no	—
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	—	2	1	no	—
196	C₄×Dic₄₃	—	2	1	no	—
197	C₄×Dic₄₃	—	2	1	no	—
198	C₄×Dic₄₃	—	4	1	no	—
199	C₄×Dic₄₃	—	4	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	C₂×C₄₃⋊C₈	—	2	1	no	—
212	C₂×C₄₃⋊C₈	—	4	4	no	—
213	C₂³×C₄₃	—	2	1	no	—
214	C₂³×C₄₃	—	2	1	no	—
215	C₂³×C₄₃	—	2	1	no	—
216	C₂³×C₄₃	—	2	1	no	—
217	C₂³×C₄₃	—	2	1	no	—
218	C₂³×C₄₃	—	2	1	no	—
219	C₂³×C₄₃	—	2	1	no	—
220	C₂³×C₄₃	—	2	1	no	—
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	1	no	—
223	C₂³×C₄₃	—	2	1	no	—
224	C₂³×C₄₃	#117	1	2	yes	—
225	C₂³×C₄₃	#131	1	2	yes	—
226	C₂³×C₄₃	#131	1	2	yes	—
227	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
228	D₄×C₄₃	—	4	4	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	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	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	#117	1	2	yes	—
249	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
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	—	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	—	2	1	no	—
273	C₂×Dic₄₃	—	2	1	no	—
274	C₂×Dic₄₃	—	2	1	no	—
275	C₂×Dic₄₃	—	2	1	no	—
276	C₂×Dic₄₃	—	2	1	no	—
277	C₂×Dic₄₃	—	4	4	no	—
278	C₂×Dic₄₃	—	4	4	no	—
279	C₂×Dic₄₃	#131	1	2	yes	—
280	C₂×Dic₄₃	#131	1	2	yes	—
281	C₈×C₄₃	—	4	1	no	—
282	C₈×C₄₃	—	4	1	no	—
283	C₈×C₄₃	—	4	1	no	—
284	C₈×C₄₃	—	4	1	no	—
285	C₄₃⋊C₈	—	4	1	no	—
286	C₄₃⋊C₈	—	4	1	no	—
287	C₄₃⋊C₈	—	4	1	no	—
288	C₄₃⋊C₈	—	4	1	no	—
289	#21997	—	43	1	no	maximal, Sylow
290	C₂²×C₄₃	—	2	2	no	—
291	C₂²×C₄₃	—	2	2	no	—
292	C₂²×C₄₃	—	2	2	no	—
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	2	2	no	—
295	C₂²×C₄₃	—	2	2	no	—
296	C₂²×C₄₃	—	4	1	no	—
297	C₂²×C₄₃	—	4	1	no	—
298	C₂²×C₄₃	—	4	1	no	—
299	C₂²×C₄₃	—	4	1	no	—
300	C₂²×C₄₃	—	4	1	no	—
301	C₂²×C₄₃	—	4	1	no	—
302	C₂²×C₄₃	—	4	1	no	—
303	C₂²×C₄₃	#433	1	4	yes	—
304	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
305	C₂²×C₄₃	#518	1	1	yes	characteristic
306	C₂²×C₄₃	#520	1	1	yes	characteristic
307	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
308	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
309	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
310	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
311	C₄×C₄₃	—	2	2	no	—
312	C₄×C₄₃	—	4	1	no	—
313	C₄×C₄₃	—	4	1	no	—
314	C₄×C₄₃	—	4	1	no	—
315	C₄×C₄₃	#538	1	1	yes	characteristic
316	C₄×C₄₃	#538	1	1	yes	characteristic
317	C₄×C₄₃	#539	1	1	yes	characteristic
318	C₄×C₄₃	#539	1	1	yes	characteristic
319	Dic₄₃	—	2	2	no	—
320	Dic₄₃	—	2	2	no	—
321	Dic₄₃	—	4	1	no	—
322	Dic₄₃	—	4	1	no	—
323	Dic₄₃	—	4	1	no	—
324	Dic₄₃	—	4	1	no	—
325	Dic₄₃	—	4	1	no	—
326	Dic₄₃	—	4	1	no	—
327	#2290	—	43	1	no	—
328	#1923	—	43	1	no	—
329	#1923	—	43	1	no	—
330	#1916	—	43	1	no	—
331	#1916	—	43	1	no	—
332	#1869	—	43	1	no	—
333	#1869	D₄₃	1	1	yes	characteristic
334	#1850	—	43	1	no	—
335	#1850	—	43	1	no	—
336	#1840	—	43	1	no	—
337	#1832	—	43	1	no	—
338	#1818	—	43	1	no	—
339	#1798	—	43	1	no	—
340	C₄×C₂²⋊C₈	—	43	1	no	—
341	C₂×#336	—	43	1	no	—
342	C₂×C₄₃	—	2	4	no	—
343	C₂×C₄₃	—	8	1	no	—
344	C₂×C₄₃	#2318	1	1	yes	characteristic
345	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
346	C₂×C₄₃	#2922	1	1	yes	characteristic
347	C₂×C₄₃	#2977	1	1	yes	characteristic
348	C₂×C₄₃	#2977	1	1	yes	characteristic
349	C₂×C₄₃	#2994	1	1	yes	characteristic
350	C₂×C₄₃	#2994	1	1	yes	characteristic
351	C₂³×C₈	—	43	1	no	—
352	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
353	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
354	C₂×#117	—	43	1	no	—
355	C₂²×C₄²	—	43	1	no	—
356	C₂×C₄⋊C₈	—	43	1	no	—
357	C₂×C₄⋊C₈	—	43	1	no	—
358	C₂×C₄⋊C₈	—	43	1	no	—
359	C₂×C₄⋊C₈	—	43	1	no	—
360	C₂×C₂²⋊C₈	—	43	1	no	—
361	C₂×C₂²⋊C₈	—	43	1	no	—
362	C₂×C₂²⋊C₈	—	43	1	no	—
363	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
366	C₂×C₄×C₈	—	43	1	no	—
367	C₂×C₄×C₈	—	43	1	no	—
368	#388	—	43	1	no	—
369	#388	—	43	1	no	—
370	#387	—	43	1	no	—
371	#387	—	43	1	no	—
372	#386	—	43	1	no	—
373	#386	—	43	1	no	—
374	#385	—	43	1	no	—
375	#385	—	43	1	no	—
376	C₄×C₄⋊C₄	—	43	1	no	—
377	C₄×C₂²⋊C₄	—	43	1	no	—
378	C₄×C₂²⋊C₄	—	43	1	no	—
379	#376	—	43	1	no	—
380	#336	—	43	1	no	—
381	#336	—	43	1	no	—
382	#336	—	43	1	no	—
383	#336	—	43	1	no	—
384	#336	—	43	1	no	—
385	#336	—	43	1	no	—
386	#336	—	43	1	no	—
387	#336	—	43	1	no	—
388	#336	—	43	1	no	—
389	#336	—	43	1	no	—
390	#336	—	43	1	no	—
391	#336	—	43	1	no	—
392	#336	C₂×D₄₃	1	1	yes	characteristic
393	#336	C₂×D₄₃	1	1	yes	characteristic
394	C₄₃	#21997	1	1	yes	characteristic, complemented, Sylow
395	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
396	C₂³×C₄	—	43	1	no	—
397	C₂³×C₄	—	43	1	no	—
398	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
399	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
400	C₂²×C₈	—	2	2	no	—
401	C₂²×C₈	—	4	1	no	—
402	C₂²×C₈	—	4	1	no	—
403	C₂²×C₈	—	43	1	no	—
404	C₂²×C₈	—	43	1	no	—
405	C₂²×C₈	—	43	1	no	—
406	C₂²×C₈	—	43	1	no	—
407	C₂²×C₈	—	86	2	no	—
408	C₂²×C₈	—	172	1	no	—
409	C₂²×C₈	—	172	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	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	#117	—	172	1	no	—
417	#117	—	172	1	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	—	43	1	no	—
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	C₄×D₄₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
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	—	43	1	no	—
436	C₂×C₄²	—	43	1	no	—
437	C₂×C₄²	—	172	1	no	—
438	C₂×C₄²	—	172	1	no	—
439	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
440	C₄⋊C₈	—	172	1	no	—
441	C₄⋊C₈	—	172	1	no	—
442	C₄⋊C₈	—	172	1	no	—
443	C₄⋊C₈	—	172	1	no	—
444	C₂²⋊C₈	—	2	2	no	—
445	C₂²⋊C₈	—	4	1	no	—
446	C₂²⋊C₈	—	4	1	no	—
447	C₂²⋊C₈	—	86	2	no	—
448	C₂²⋊C₈	—	172	1	no	—
449	C₂²⋊C₈	—	172	1	no	—
450	C₄×C₈	—	172	1	no	—
451	C₄×C₈	—	172	1	no	—
452	#95	—	43	1	no	—
453	#95	—	43	1	no	—
454	#95	—	43	1	no	—
455	#95	—	43	1	no	—
456	#95	—	43	1	no	—
457	#95	—	43	1	no	—
458	#95	—	43	1	no	—
459	#95	—	43	1	no	—
460	#95	—	43	1	no	—
461	#95	—	43	1	no	—
462	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
463	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	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	—	43	1	no	—
484	C₂²×C₄	—	43	1	no	—
485	C₂²×C₄	—	86	2	no	—
486	C₂²×C₄	—	86	2	no	—
487	C₂²×C₄	—	86	2	no	—
488	C₂²×C₄	—	86	2	no	—
489	C₂²×C₄	—	172	1	no	—
490	C₂²×C₄	—	172	1	no	—
491	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
495	C₂²×C₄	#10621900	1	2	yes	—
496	C₂²×C₄	#10621900	1	2	yes	—
497	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	4	4	no	—
511	C₂×C₈	—	86	1	no	—
512	C₂×C₈	—	86	1	no	—
513	C₂×C₈	—	86	1	no	—
514	C₂×C₈	—	86	1	no	—
515	C₂×C₈	—	86	1	no	—
516	C₂×C₈	—	86	1	no	—
517	C₂×C₈	—	86	1	no	—
518	C₂×C₈	—	86	1	no	—
519	C₂×C₈	—	86	1	no	—
520	C₂×C₈	—	86	1	no	—
521	C₂×C₈	—	86	1	no	—
522	C₂×C₈	—	86	1	no	—
523	C₂×C₈	—	172	4	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	86	2	no	—
526	C₄⋊C₄	—	86	2	no	—
527	C₄⋊C₄	—	172	1	no	—
528	C₄⋊C₄	—	172	1	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	86	2	no	—
532	C₂²⋊C₄	—	86	2	no	—
533	C₂²⋊C₄	—	86	2	no	—
534	C₂²⋊C₄	—	86	2	no	—
535	C₂²⋊C₄	—	172	1	no	—
536	C₂²⋊C₄	—	172	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	86	1	no	—
540	C₄²	—	86	1	no	—
541	C₄²	—	86	1	no	—
542	C₄²	—	86	1	no	—
543	C₄²	—	86	1	no	—
544	C₄²	—	86	1	no	—
545	C₄²	—	86	1	no	—
546	C₄²	—	86	1	no	—
547	C₄²	—	172	1	no	—
548	C₄²	—	172	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	1	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	#13063281	1	2	yes	—
561	C₂³	#13063331	1	2	yes	—
562	C₂³	#13063333	1	2	yes	—
563	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
564	D₄	—	4	4	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	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	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	43	2	no	—
585	C₂×C₄	—	43	2	no	—
586	C₂×C₄	—	86	1	no	—
587	C₂×C₄	—	86	1	no	—
588	C₂×C₄	—	86	1	no	—
589	C₂×C₄	—	86	1	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	—	86	1	no	—
607	C₂×C₄	—	86	1	no	—
608	C₂×C₄	—	172	4	no	—
609	C₂×C₄	—	172	4	no	—
610	C₂×C₄	#13063281	1	2	yes	—
611	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
612	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
613	C₂×C₄	#13063370	1	1	yes	characteristic
614	C₂×C₄	#13063370	1	1	yes	characteristic
615	C₂×C₄	#13063371	1	1	yes	characteristic
616	C₂×C₄	#13063372	1	1	yes	characteristic
617	C₈	—	4	1	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₈	—	4	1	no	—
621	C₈	—	172	1	no	—
622	C₈	—	172	1	no	—
623	C₈	—	172	1	no	—
624	C₈	—	172	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	#14582957	1	4	yes	—
639	C₂²	C₂×#13063281	1	1	yes	characteristic
640	C₂²	#14583371	1	1	yes	characteristic
641	C₂²	#14583378	1	1	yes	characteristic
642	C₂²	#131×D₄₃	1	1	yes	characteristic
643	C₂²	#131×D₄₃	1	1	yes	characteristic
644	C₂²	C₂×#13063331	1	1	yes	characteristic
645	C₂²	C₂×#13063333	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	86	2	no	—
651	C₄	—	86	2	no	—
652	C₄	—	172	1	no	—
653	C₄	—	172	1	no	—
654	C₄	—	172	1	no	—
655	C₄	—	172	1	no	—
656	C₄	—	172	1	no	—
657	C₄	—	172	1	no	—
658	C₄	#14583484	1	1	yes	characteristic
659	C₄	#14583486	1	1	yes	characteristic
660	C₄	#14583493	1	1	yes	characteristic
661	C₄	#14583494	1	1	yes	characteristic
662	C₂	—	2	4	no	—
663	C₂	—	8	1	no	—
664	C₂	#19137221	1	1	yes	characteristic
665	C₂	C₂×#14582957	1	1	yes	characteristic
666	C₂	#19143235	1	1	yes	characteristic
667	C₂	#19143646	1	1	yes	characteristic
668	C₂	#19143648	1	1	yes	characteristic
669	C₂	#19143748	1	1	yes	characteristic
670	C₂	#19143752	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1869	C₂
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1869	D₄₃
hypocenter	C₄₃	#21997
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1869

Complements

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

N	H ≅ G/N	type
2. #19135204	C₂	semidirect
3. #19135198	C₂	semidirect
4. #19135153	C₂	semidirect
5. #19135151	C₂	semidirect
7. #19134773	C₂	semidirect
8. #19134772	C₂	semidirect
9. #19134739	C₂	semidirect
10. #19134713	C₂	semidirect
11. #19134664	C₂	semidirect
12. #19134577	C₂	semidirect
13. C₂²⋊C₈×Dic₄₃	C₂	semidirect
14. C₂×#14582653	C₂	semidirect
394. C₄₃	#21997	semidirect

Maximal subgroups

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

subgroup	index
#19137040	2
#19135204	2
#19135198	2
#19135153	2
#19135151	2
#19134888	2
#19134773	2
#19134772	2
#19134739	2
#19134713	2
#19134664	2
#19134577	2
C₂²⋊C₈×Dic₄₃	2
C₂×#14582653	2
C₄₃×#1869	2
#21997	43