Subgroups — #25095116

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583000	C₂	1	1	yes	maximal, characteristic
2	C₂×SD₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19136960	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136956	C₂	1	1	yes	maximal, characteristic
5	#19134494	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134492	C₂	1	1	yes	maximal, characteristic, complemented
7	#107×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134427	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134422	C₂	1	1	yes	maximal, characteristic
10	#103×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#13063249	C₂	1	1	yes	maximal, characteristic, complemented
12	#102×Dic₄₃	C₂	1	1	yes	maximal, characteristic
13	C₄×#13063246	C₂	1	1	yes	maximal, characteristic
14	#19134283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₃×#440	C₂	1	1	yes	maximal, characteristic
16	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×D₄×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×Dic₄₃	C₂²	1	1	yes	characteristic
20	#14583000	C₄	1	8	yes	complemented
21	SD₁₆×Dic₄₃	C₄	1	8	yes	complemented
22	C₂×#13063259	C₂²	1	1	yes	characteristic
23	C₂×#13063257	C₂²	1	1	yes	characteristic
24	C₂×#13063249	C₂²	1	1	yes	characteristic
25	C₂×#13063249	C₂²	1	1	yes	characteristic
26	C₂×#13063246	C₂²	1	1	yes	characteristic
27	C₂×#13063246	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×#13063235	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₄⋊C₄×Dic₄₃	—	2	1	no	—
34	C₄⋊C₄×Dic₄₃	—	2	1	no	—
35	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₄₃	—	2	1	no	—
40	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
42	C₂²⋊C₄×Dic₄₃	—	2	1	no	—
43	C₂²⋊C₄×Dic₄₃	—	2	1	no	—
44	C₄×C₂²⋊Dic₄₃	—	2	1	no	—
45	#14582745	—	2	1	no	—
46	#14582745	C₂²	1	1	yes	characteristic
47	C₂×C₄₃⋊#95	—	2	1	no	—
48	#14582662	C₂²	1	1	yes	characteristic
49	#14582662	C₂²	1	1	yes	characteristic
50	#14582661	C₂²	1	1	yes	characteristic
51	#14582661	C₂²	1	1	yes	characteristic
52	#14582661	C₂²	1	1	yes	characteristic
53	#14582661	C₂²	1	1	yes	characteristic
54	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#440	C₄	1	8	yes	complemented
58	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
60	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
61	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
62	C₂³×Dic₄₃	—	2	1	no	—
63	C₂³×Dic₄₃	—	2	1	no	—
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
66	Q₈×Dic₄₃	—	2	2	no	—
67	Q₈×Dic₄₃	—	2	2	no	—
68	Q₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
69	Q₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
70	D₄×Dic₄₃	—	2	2	no	—
71	D₄×Dic₄₃	—	2	2	no	—
72	D₄×Dic₄₃	C₂×C₄	1	4	yes	—
73	D₄×Dic₄₃	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
81	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
82	C₂×C₄×Dic₄₃	—	2	1	no	—
83	C₂×C₄×Dic₄₃	—	2	1	no	—
84	C₂×C₄×Dic₄₃	—	2	1	no	—
85	C₂×C₄×Dic₄₃	—	2	1	no	—
86	C₂×C₄×Dic₄₃	—	2	1	no	—
87	C₂×C₄×Dic₄₃	—	2	1	no	—
88	C₂×C₄×Dic₄₃	—	2	1	no	—
89	C₂×C₄×Dic₄₃	—	2	1	no	—
90	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
92	#13063259	C₂×C₄	1	4	yes	complemented
93	#13063257	C₂×C₄	1	4	yes	complemented
94	#13063249	C₂×C₄	1	4	yes	complemented
95	#13063249	C₂×C₄	1	4	yes	complemented
96	#13063246	C₂×C₄	1	4	yes	—
97	#13063246	C₂×C₄	1	4	yes	—
98	#13063235	—	2	2	no	—
99	#13063235	C₂×C₄	1	4	yes	complemented
100	C₄×C₄₃⋊C₈	—	2	2	no	—
101	C₈×Dic₄₃	—	2	2	no	—
102	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
103	C₄₃⋊#95	—	2	1	no	—
104	C₄₃⋊#95	—	2	1	no	—
105	C₄₃⋊#95	—	2	1	no	—
106	C₄₃⋊#95	—	2	1	no	—
107	C₄₃⋊#95	—	2	1	no	—
108	C₄₃⋊#95	—	2	1	no	—
109	C₄₃⋊#95	D₄	1	1	yes	characteristic
110	C₄₃⋊#95	D₄	1	1	yes	characteristic
111	C₄₃⋊#95	D₄	1	1	yes	characteristic
112	C₄₃⋊#95	D₄	1	1	yes	characteristic
113	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₄₃	—	2	1	no	—
116	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
117	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
118	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₄₃	—	2	2	no	—
122	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
123	C₄×D₄×C₄₃	—	2	2	no	—
124	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
125	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
129	C₂×C₄²×C₄₃	—	2	1	no	—
130	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
131	#107×C₄₃	C₂×C₄	1	4	yes	complemented
132	#103×C₄₃	C₂×C₄	1	4	yes	complemented
133	#102×C₄₃	C₂×C₄	1	4	yes	—
134	#97×C₄₃	C₂×C₄	1	4	yes	complemented
135	C₂⁴×C₄₃	—	2	1	no	—
136	C₂×Q₈×C₄₃	—	2	1	no	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	1	no	—
139	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₄₃	—	2	1	no	—
143	C₂×D₄×C₄₃	—	2	1	no	—
144	C₂×D₄×C₄₃	—	2	1	no	—
145	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₄₃	—	2	4	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	8	1	no	—
153	C₂²×C₄×C₄₃	—	8	1	no	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²×Dic₄₃	—	2	4	no	—
158	C₂²×Dic₄₃	—	2	4	no	—
159	C₂²×Dic₄₃	—	2	1	no	—
160	C₂²×Dic₄₃	—	2	1	no	—
161	C₂²×Dic₄₃	—	2	1	no	—
162	C₂²×Dic₄₃	—	2	1	no	—
163	C₂²×Dic₄₃	—	8	1	no	—
164	C₂²×Dic₄₃	—	8	1	no	—
165	C₂²×Dic₄₃	—	8	1	no	—
166	C₂²×Dic₄₃	—	8	1	no	—
167	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
171	SD₁₆×C₄₃	C₄²	1	16	yes	complemented
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
178	C₄⋊C₄×C₄₃	—	2	4	no	—
179	C₄⋊C₄×C₄₃	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
182	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
183	C₂²⋊C₄×C₄₃	—	2	4	no	—
184	C₄²×C₄₃	—	2	4	no	—
185	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
186	C₄²×C₄₃	#41	1	2	yes	—
187	C₂²⋊Dic₄₃	—	2	4	no	—
188	C₂²⋊Dic₄₃	—	2	4	no	—
189	C₄⋊Dic₄₃	—	2	1	no	—
190	C₄⋊Dic₄₃	—	2	1	no	—
191	C₄⋊Dic₄₃	—	2	1	no	—
192	C₄⋊Dic₄₃	—	2	1	no	—
193	C₄⋊Dic₄₃	—	2	4	no	—
194	C₄⋊Dic₄₃	—	2	4	no	—
195	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
196	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
197	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
198	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
199	C₄×Dic₄₃	—	2	4	no	—
200	C₄×Dic₄₃	—	2	4	no	—
201	C₄×Dic₄₃	—	8	1	no	—
202	C₄×Dic₄₃	—	8	1	no	—
203	C₄×Dic₄₃	—	8	1	no	—
204	C₄×Dic₄₃	—	8	1	no	—
205	C₄×Dic₄₃	—	8	1	no	—
206	C₄×Dic₄₃	—	8	1	no	—
207	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
208	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
209	C₄×Dic₄₃	#41	1	2	yes	—
210	C₄×Dic₄₃	#41	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
216	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
217	C₂³×C₄₃	—	2	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	4	1	no	—
221	C₂³×C₄₃	—	4	1	no	—
222	C₂³×C₄₃	—	4	1	no	—
223	C₂³×C₄₃	—	4	1	no	—
224	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₄₃	—	2	2	no	—
226	Q₈×C₄₃	—	2	2	no	—
227	Q₈×C₄₃	—	2	2	no	—
228	Q₈×C₄₃	C₂×C₄²	1	4	yes	—
229	D₄×C₄₃	—	2	2	no	—
230	D₄×C₄₃	—	2	2	no	—
231	D₄×C₄₃	—	2	2	no	—
232	D₄×C₄₃	C₂×C₄²	1	4	yes	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	2	2	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	2	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	8	4	no	—
247	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂³×C₄	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×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	2	no	—
264	C₂×Dic₄₃	—	2	2	no	—
265	C₂×Dic₄₃	—	2	2	no	—
266	C₂×Dic₄₃	—	2	2	no	—
267	C₂×Dic₄₃	—	4	1	no	—
268	C₂×Dic₄₃	—	4	1	no	—
269	C₂×Dic₄₃	—	4	1	no	—
270	C₂×Dic₄₃	—	4	1	no	—
271	C₂×Dic₄₃	—	4	1	no	—
272	C₂×Dic₄₃	—	4	1	no	—
273	C₂×Dic₄₃	—	4	1	no	—
274	C₂×Dic₄₃	—	4	1	no	—
275	C₂×Dic₄₃	—	8	4	no	—
276	C₂×Dic₄₃	—	8	4	no	—
277	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
278	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
279	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
280	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
281	C₈×C₄₃	—	2	2	no	—
282	C₈×C₄₃	C₂×C₄²	1	4	yes	—
283	C₄₃⋊C₈	—	2	2	no	—
284	C₄₃⋊C₈	—	2	2	no	—
285	#20504	—	43	1	no	maximal, Sylow
286	C₂²×C₄₃	—	2	4	no	—
287	C₂²×C₄₃	—	4	2	no	—
288	C₂²×C₄₃	—	4	2	no	—
289	C₂²×C₄₃	—	4	2	no	—
290	C₂²×C₄₃	—	4	2	no	—
291	C₂²×C₄₃	—	4	2	no	—
292	C₂²×C₄₃	—	4	2	no	—
293	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×C₄₃	#576	1	1	yes	characteristic
297	C₂²×C₄₃	#577	1	1	yes	characteristic
298	C₂²×C₄₃	#577	1	1	yes	characteristic
299	C₂²×C₄₃	#578	1	1	yes	characteristic
300	C₄×C₄₃	—	2	2	no	—
301	C₄×C₄₃	—	2	2	no	—
302	C₄×C₄₃	—	2	4	no	—
303	C₄×C₄₃	—	4	2	no	—
304	C₄×C₄₃	—	4	2	no	—
305	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
306	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
307	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
308	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
309	Dic₄₃	—	2	2	no	—
310	Dic₄₃	—	2	2	no	—
311	Dic₄₃	—	2	2	no	—
312	Dic₄₃	—	2	2	no	—
313	Dic₄₃	—	4	2	no	—
314	Dic₄₃	—	4	2	no	—
315	Dic₄₃	—	4	2	no	—
316	Dic₄₃	—	4	2	no	—
317	C₂×#440	—	43	1	no	—
318	C₂×#440	D₄₃	1	1	yes	characteristic
319	C₂×C₄×SD₁₆	—	43	1	no	—
320	#2276	—	43	1	no	—
321	#2275	—	43	1	no	—
322	#1776	—	43	1	no	—
323	#1776	—	43	1	no	—
324	C₄×#107	—	43	1	no	—
325	#1763	—	43	1	no	—
326	#1762	—	43	1	no	—
327	C₄×#103	—	43	1	no	—
328	C₄×#103	—	43	1	no	—
329	C₄×#102	—	43	1	no	—
330	C₄×#102	—	43	1	no	—
331	#1726	—	43	1	no	—
332	C₂×C₄₃	—	4	4	no	—
333	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
334	C₂×C₄₃	#2946	1	1	yes	characteristic
335	C₂×C₄₃	#2946	1	1	yes	characteristic
336	C₂×C₄₃	#2947	1	1	yes	characteristic
337	C₂×C₄₃	#2947	1	1	yes	characteristic
338	C₂×C₄₃	#2949	1	1	yes	characteristic
339	C₂×C₄₃	#2951	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
341	C₂×C₄×Q₈	—	43	1	no	—
342	C₂×C₄×Q₈	—	43	1	no	—
343	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
344	C₂×C₄×D₄	—	43	1	no	—
345	C₂×C₄×D₄	—	43	1	no	—
346	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
347	#440	—	43	8	no	—
348	#440	Dic₄₃	1	8	yes	complemented
349	C₄×SD₁₆	—	43	8	no	—
350	C₂×#107	—	43	1	no	—
351	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
352	C₂×#106	—	43	1	no	—
353	C₂×#103	—	43	1	no	—
354	C₂×#103	—	43	1	no	—
355	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
356	C₂×#102	—	43	1	no	—
357	C₂×#102	—	43	1	no	—
358	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
359	C₂×#97	—	43	1	no	—
360	C₂×#97	—	43	1	no	—
361	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
362	C₂×C₄×C₈	—	43	1	no	—
363	C₂×C₄×C₈	—	43	1	no	—
364	C₂×C₄×C₈	—	43	1	no	—
365	C₄×C₄⋊C₄	—	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	—	43	1	no	—
370	C₄×C₄⋊C₄	—	43	1	no	—
371	C₄×C₄⋊C₄	—	86	1	no	—
372	C₄×C₄⋊C₄	—	86	1	no	—
373	C₄×C₄⋊C₄	—	86	1	no	—
374	C₄×C₂²⋊C₄	—	86	1	no	—
375	C₄×C₂²⋊C₄	—	86	1	no	—
376	C₄×C₂²⋊C₄	—	86	1	no	—
377	#376	—	43	1	no	—
378	#376	—	86	1	no	—
379	C₂×#95	—	86	1	no	—
380	#340	—	43	1	no	—
381	#340	—	43	1	no	—
382	#340	—	43	1	no	—
383	#340	—	43	1	no	—
384	#340	—	43	1	no	—
385	#340	—	43	1	no	—
386	C₄₃	#20504	1	1	yes	characteristic, complemented, Sylow
387	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
388	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	86	1	no	—
391	C₂³×C₄	—	86	1	no	—
392	C₂×SD₁₆	C₄×D₄₃	1	4	yes	—
393	C₂×SD₁₆	C₄×D₄₃	1	4	yes	—
394	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
395	C₂²×C₈	—	43	1	no	—
396	C₂²×C₈	—	43	1	no	—
397	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₄×Q₈	—	2	2	no	—
400	C₄×Q₈	—	43	4	no	—
401	C₄×Q₈	—	43	4	no	—
402	C₄×Q₈	—	86	2	no	—
403	C₄×Q₈	—	86	2	no	—
404	C₄×Q₈	C₂×Dic₄₃	1	4	yes	complemented
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	43	4	no	—
407	C₄×D₄	—	43	4	no	—
408	C₄×D₄	—	86	2	no	—
409	C₄×D₄	—	86	2	no	—
410	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	43	1	no	—
413	C₂×C₄⋊C₄	—	43	1	no	—
414	C₂×C₄⋊C₄	—	43	1	no	—
415	C₂×C₄⋊C₄	—	43	1	no	—
416	C₂×C₄⋊C₄	—	86	1	no	—
417	C₂×C₄⋊C₄	—	86	1	no	—
418	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	86	1	no	—
422	C₂×C₂²⋊C₄	—	86	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	43	1	no	—
425	C₂×C₄²	—	43	1	no	—
426	C₂×C₄²	—	86	1	no	—
427	C₂×C₄²	—	86	1	no	—
428	C₂×C₄²	—	86	1	no	—
429	C₂×C₄²	—	86	1	no	—
430	C₂×C₄²	—	86	1	no	—
431	C₂×C₄²	—	86	1	no	—
432	C₂×C₄²	—	86	1	no	—
433	C₂×C₄²	—	86	1	no	—
434	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
435	#107	—	43	4	no	—
436	#107	C₂×Dic₄₃	1	4	yes	complemented
437	#106	—	43	4	no	—
438	#103	—	43	4	no	—
439	#103	—	43	4	no	—
440	#103	C₂×Dic₄₃	1	4	yes	complemented
441	#102	—	43	4	no	—
442	#102	—	43	4	no	—
443	#102	C₂×Dic₄₃	1	4	yes	—
444	#97	—	43	4	no	—
445	#97	—	86	2	no	—
446	#97	C₂×Dic₄₃	1	4	yes	complemented
447	C₄×C₈	—	43	4	no	—
448	C₄×C₈	—	86	2	no	—
449	C₄×C₈	—	86	2	no	—
450	#95	—	43	1	no	—
451	#95	—	43	1	no	—
452	#95	—	43	1	no	—
453	#95	—	43	1	no	—
454	#95	—	86	1	no	—
455	#95	—	86	1	no	—
456	#95	—	86	1	no	—
457	#95	—	86	1	no	—
458	#95	—	86	1	no	—
459	#95	—	86	1	no	—
460	C₂⁴	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
465	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
466	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
471	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
472	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	8	1	no	—
478	C₂²×C₄	—	8	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	4	no	—
484	C₂²×C₄	—	86	4	no	—
485	C₂²×C₄	—	86	1	no	—
486	C₂²×C₄	—	86	1	no	—
487	C₂²×C₄	—	86	1	no	—
488	C₂²×C₄	—	86	1	no	—
489	C₂²×C₄	—	344	1	no	—
490	C₂²×C₄	—	344	1	no	—
491	C₂²×C₄	—	344	1	no	—
492	C₂²×C₄	—	344	1	no	—
493	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
494	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
495	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
496	SD₁₆	C₄×Dic₄₃	1	16	yes	complemented
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	43	2	no	—
500	C₂×C₈	—	43	2	no	—
501	C₂×C₈	—	86	1	no	—
502	C₂×C₈	—	86	1	no	—
503	C₂×C₈	—	86	1	no	—
504	C₂×C₈	—	86	1	no	—
505	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
506	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
507	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
508	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	43	2	no	—
513	C₄⋊C₄	—	43	2	no	—
514	C₄⋊C₄	—	43	2	no	—
515	C₄⋊C₄	—	43	2	no	—
516	C₄⋊C₄	—	86	4	no	—
517	C₄⋊C₄	—	86	4	no	—
518	C₄⋊C₄	—	86	1	no	—
519	C₄⋊C₄	—	86	1	no	—
520	C₄⋊C₄	—	86	1	no	—
521	C₄⋊C₄	—	86	1	no	—
522	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
523	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	86	4	no	—
526	C₂²⋊C₄	—	86	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	43	2	no	—
529	C₄²	—	43	2	no	—
530	C₄²	—	43	2	no	—
531	C₄²	—	43	2	no	—
532	C₄²	—	86	4	no	—
533	C₄²	—	86	4	no	—
534	C₄²	—	344	1	no	—
535	C₄²	—	344	1	no	—
536	C₄²	—	344	1	no	—
537	C₄²	—	344	1	no	—
538	C₄²	—	344	1	no	—
539	C₄²	—	344	1	no	—
540	C₄²	#10621900	1	2	yes	—
541	C₄²	C₂²×Dic₄₃	1	2	yes	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
550	Q₈	—	2	2	no	—
551	Q₈	—	2	2	no	—
552	Q₈	—	2	2	no	—
553	Q₈	C₂×C₄×Dic₄₃	1	4	yes	—
554	D₄	—	2	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	2	2	no	—
557	D₄	C₂×C₄×Dic₄₃	1	4	yes	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	8	4	no	—
572	C₂×C₄	—	43	2	no	—
573	C₂×C₄	—	43	2	no	—
574	C₂×C₄	—	43	2	no	—
575	C₂×C₄	—	43	2	no	—
576	C₂×C₄	—	86	1	no	—
577	C₂×C₄	—	86	1	no	—
578	C₂×C₄	—	86	1	no	—
579	C₂×C₄	—	86	1	no	—
580	C₂×C₄	—	86	1	no	—
581	C₂×C₄	—	86	1	no	—
582	C₂×C₄	—	86	1	no	—
583	C₂×C₄	—	86	1	no	—
584	C₂×C₄	—	86	2	no	—
585	C₂×C₄	—	86	2	no	—
586	C₂×C₄	—	86	2	no	—
587	C₂×C₄	—	86	2	no	—
588	C₂×C₄	—	344	4	no	—
589	C₂×C₄	—	344	4	no	—
590	C₂×C₄	—	172	1	no	—
591	C₂×C₄	—	172	1	no	—
592	C₂×C₄	—	172	1	no	—
593	C₂×C₄	—	172	1	no	—
594	C₂×C₄	—	172	1	no	—
595	C₂×C₄	—	172	1	no	—
596	C₂×C₄	—	172	1	no	—
597	C₂×C₄	—	172	1	no	—
598	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
599	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
600	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
602	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
603	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
604	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
606	C₈	—	2	2	no	—
607	C₈	—	86	2	no	—
608	C₈	—	86	2	no	—
609	C₈	C₂×C₄×Dic₄₃	1	4	yes	—
610	C₂²	—	2	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
618	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
619	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
620	C₂²	#14583703	1	1	yes	characteristic
621	C₂²	#14583708	1	1	yes	characteristic
622	C₂²	#14583709	1	1	yes	characteristic
623	C₂²	#14583715	1	1	yes	characteristic
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	86	2	no	—
630	C₄	—	86	2	no	—
631	C₄	—	86	2	no	—
632	C₄	—	86	2	no	—
633	C₄	—	172	2	no	—
634	C₄	—	172	2	no	—
635	C₄	—	172	2	no	—
636	C₄	—	172	2	no	—
637	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
638	C₄	C₄×#10621900	1	1	yes	characteristic
639	C₄	C₄×#10621900	1	1	yes	characteristic
640	C₄	#41×Dic₄₃	1	1	yes	characteristic
641	C₂	—	4	4	no	—
642	C₂	C₄×D₄×Dic₄₃	1	1	yes	characteristic
643	C₂	#19143426	1	1	yes	characteristic
644	C₂	#19143428	1	1	yes	characteristic
645	C₂	#19143435	1	1	yes	characteristic
646	C₂	#19143439	1	1	yes	characteristic
647	C₂	#19143451	1	1	yes	characteristic
648	C₂	#19143467	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#440	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#440	D₄₃
hypocenter	C₄₃	#20504
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#440

Complements

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

N	H ≅ G/N	type
3. #19136960	C₂	semidirect
5. #19134494	C₂	semidirect
6. #19134492	C₂	semidirect
7. #107×Dic₄₃	C₂	semidirect
8. #19134427	C₂	semidirect
10. #103×Dic₄₃	C₂	semidirect
11. C₄×#13063249	C₂	semidirect
14. #19134283	C₂	semidirect
20. #14583000	C₄	semidirect
21. SD₁₆×Dic₄₃	C₄	semidirect
57. C₄₃×#440	C₄	semidirect
68. Q₈×Dic₄₃	C₂×C₄	semidirect
69. Q₈×Dic₄₃	C₂×C₄	semidirect
92. #13063259	C₂×C₄	semidirect
93. #13063257	C₂×C₄	semidirect
94. #13063249	C₂×C₄	semidirect
95. #13063249	C₂×C₄	semidirect
99. #13063235	C₂×C₄	semidirect
102. C₈×Dic₄₃	C₂×C₄	semidirect
122. C₄×Q₈×C₄₃	C₂×C₄	semidirect
131. #107×C₄₃	C₂×C₄	semidirect
132. #103×C₄₃	C₂×C₄	semidirect
134. #97×C₄₃	C₂×C₄	semidirect
171. SD₁₆×C₄₃	C₄²	semidirect
348. #440	Dic₄₃	semidirect
386. C₄₃	#20504	semidirect
404. C₄×Q₈	C₂×Dic₄₃	semidirect
436. #107	C₂×Dic₄₃	semidirect
440. #103	C₂×Dic₄₃	semidirect
446. #97	C₂×Dic₄₃	semidirect
496. SD₁₆	C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583000	2
C₂×SD₁₆×Dic₄₃	2
#19136960	2
#19136956	2
#19134494	2
#19134492	2
#107×Dic₄₃	2
#19134427	2
#19134422	2
#103×Dic₄₃	2
C₄×#13063249	2
#102×Dic₄₃	2
C₄×#13063246	2
#19134283	2
C₂×C₄₃×#440	2
#20504	43