Subgroups — #25067517

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144622	C₂	1	1	yes	maximal, characteristic
2	M₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133483	C₂	1	2	yes	maximal, complemented
4	#19133436	C₂	1	2	yes	maximal, complemented
5	#19133431	C₂	1	2	yes	maximal, complemented
6	C₈×#10621883	C₂	1	2	yes	maximal, complemented
7	#19133365	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133046	C₂	1	1	yes	maximal, characteristic
9	C₂×#14582629	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2935	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	#14583215	C₄	1	2	yes	—
14	#14583181	C₄	1	1	yes	characteristic
15	#14583181	C₄	1	1	yes	characteristic
16	#14583096	C₄	1	1	yes	characteristic
17	#14583096	C₄	1	1	yes	characteristic
18	#14583037	C₄	1	2	yes	—
19	#14583029	C₂²	1	2	yes	—
20	#14583027	—	2	2	no	—
21	C₈×Dic₈₆	C₂²	1	2	yes	—
22	C₄×#10621883	C₂²	1	2	yes	—
23	C₄×#10621883	C₂²	1	2	yes	—
24	#14582952	C₂²	1	1	yes	characteristic
25	#14582923	C₂²	1	1	yes	characteristic
26	#14582922	—	2	1	no	—
27	M₁₆×Dic₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582649	C₂²	1	2	yes	—
30	#14582649	C₂²	1	2	yes	—
31	#14582629	C₂²	1	1	yes	characteristic
32	#14582629	C₂²	1	1	yes	characteristic
33	#14582629	C₂²	1	1	yes	characteristic
34	#14582629	C₂²	1	1	yes	characteristic
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
37	#14582620	C₂²	1	2	yes	—
38	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
39	C₂×#131×C₄₃	—	2	1	no	—
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#436	C₂²	1	2	yes	—
42	C₄₃×#435	—	2	2	no	—
43	C₈×D₄×C₄₃	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#408	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#10621883	C₂×C₄	1	2	yes	—
49	C₂×#10621883	C₂×C₄	1	2	yes	—
50	C₂×#10621877	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₄×Dic₈₆	—	2	1	no	—
53	C₄×Dic₈₆	—	2	1	no	—
54	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
57	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂×Dic₄₃⋊C₄	—	2	1	no	—
60	C₂×C₄×Dic₄₃	—	2	1	no	—
61	#13063256	C₂×C₄	1	2	yes	—
62	#13063256	C₂×C₄	1	2	yes	—
63	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	Dic₄₃⋊C₈	—	2	2	no	—
68	Dic₄₃⋊C₈	—	2	2	no	—
69	#13063248	C₂×C₄	1	2	yes	—
70	#13063248	C₂×C₄	1	2	yes	—
71	#13063246	C₂×C₄	1	2	yes	—
72	#13063246	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
74	#13063235	—	2	2	no	—
75	C₄×C₄₃⋊C₈	—	2	1	no	—
76	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
79	C₈×Dic₄₃	—	2	2	no	—
80	C₂×#41×C₄₃	—	2	1	no	—
81	#131×C₄₃	—	4	4	no	—
82	C₂×M₁₆×C₄₃	—	2	2	no	—
83	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	—	2	2	no	—
87	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
88	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
89	#124×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₄₃	—	2	1	no	—
93	C₄×D₄×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	1	no	—
96	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₄₃	—	2	2	no	—
99	C₂²⋊C₈×C₄₃	—	2	2	no	—
100	#97×C₄₃	D₄	1	2	yes	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	#41×C₄₃	—	4	2	no	—
103	#41×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂²×Dic₄₃	—	2	1	no	—
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂×Dic₈₆	—	2	2	no	—
116	C₂×Dic₈₆	—	2	1	no	—
117	C₂×Dic₈₆	—	4	1	no	—
118	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	4	4	no	—
122	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	4	2	no	—
126	C₂×C₈×C₄₃	—	4	4	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₃	—	2	2	no	—
132	C₂²⋊C₄×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	#41	1	1	yes	characteristic
136	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
137	#10621883	—	2	4	no	—
138	#10621883	—	4	2	no	—
139	C₄⋊Dic₄₃	—	2	1	no	—
140	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
142	Dic₄₃⋊C₄	—	2	1	no	—
143	Dic₄₃⋊C₄	—	2	1	no	—
144	Dic₄₃⋊C₄	—	2	1	no	—
145	Dic₄₃⋊C₄	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	#10621877	—	4	2	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	1	no	—
154	C₂×C₄₃⋊C₈	—	4	2	no	—
155	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	4	2	no	—
160	D₄×C₄₃	—	2	2	no	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	4	4	no	—
163	D₄×C₄₃	—	4	2	no	—
164	D₄×C₄₃	—	8	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₄₃	—	2	1	no	—
180	C₂×Dic₄₃	—	2	1	no	—
181	C₂×Dic₄₃	—	2	1	no	—
182	C₂×Dic₄₃	—	2	1	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	8	1	no	—
185	Dic₈₆	—	2	1	no	—
186	Dic₈₆	—	2	1	no	—
187	Dic₈₆	—	2	1	no	—
188	Dic₈₆	—	4	2	no	—
189	Dic₈₆	#131	1	2	yes	complemented
190	C₈×C₄₃	—	2	2	no	—
191	C₈×C₄₃	—	4	1	no	—
192	C₈×C₄₃	—	4	1	no	—
193	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
194	C₄₃⋊C₈	—	2	2	no	—
195	C₄₃⋊C₈	—	2	2	no	—
196	C₄₃⋊C₈	—	2	2	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	C₄₃⋊C₈	—	4	2	no	—
199	#17997	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	4	2	no	—
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
206	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	4	2	no	—
211	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
212	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
213	C₄×C₄₃	#568	1	1	yes	characteristic
214	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
216	Dic₄₃	—	2	2	no	—
217	Dic₄₃	—	4	1	no	—
218	Dic₄₃	—	4	1	no	—
219	Dic₄₃	—	4	1	no	—
220	#3103	—	43	1	no	—
221	Q₈×M₁₆	—	43	1	no	—
222	#2935	D₄₃	1	1	yes	characteristic
223	#1590	—	43	2	no	—
224	#1583	—	43	2	no	—
225	#1582	—	43	2	no	—
226	C₈×SD₁₆	—	43	2	no	—
227	#1570	—	43	1	no	—
228	#1492	—	43	1	no	—
229	C₂×Q₈⋊C₈	—	43	1	no	—
230	C₈×M₁₆	—	43	1	no	—
231	C₂×C₄₃	—	2	2	no	—
232	C₂×C₄₃	—	8	2	no	—
233	C₂×C₄₃	#2933	1	1	yes	characteristic
234	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
235	C₂×C₄₃	#2956	1	1	yes	characteristic
236	C₂×#131	—	2	1	no	—
237	#532	C₂×D₄₃	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	43	1	no	—
239	#481	—	43	2	no	—
240	#475	—	43	1	no	—
241	#475	—	43	1	no	—
242	#460	—	43	1	no	—
243	#460	—	43	1	no	—
244	#448	—	43	2	no	—
245	#446	—	43	2	no	—
246	#446	—	86	2	no	—
247	C₈×Q₈	—	43	2	no	—
248	C₄×SD₁₆	—	43	2	no	—
249	C₄×SD₁₆	—	43	2	no	—
250	#436	C₂×D₄₃	1	2	yes	—
251	#435	—	2	2	no	—
252	C₈×D₄	C₂×D₄₃	1	2	yes	—
253	#431	—	43	1	no	—
254	#423	—	43	1	no	—
255	#423	—	86	1	no	—
256	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
257	#408	—	2	1	no	—
258	C₄×M₁₆	—	86	1	no	—
259	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
260	C₂×C₄×C₈	—	43	1	no	—
261	#334	—	43	2	no	—
262	#334	—	43	2	no	—
263	Q₈⋊C₈	—	43	1	no	—
264	Q₈⋊C₈	—	43	1	no	—
265	Q₈⋊C₈	—	43	1	no	—
266	Q₈⋊C₈	—	43	1	no	—
267	D₄⋊C₈	—	43	2	no	—
268	D₄⋊C₈	—	43	2	no	—
269	#322	—	43	2	no	—
270	C₈²	—	43	2	no	—
271	C₄₃	#17997	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	43	1	no	—
274	C₂×SD₁₆	—	43	2	no	—
275	C₂×SD₁₆	—	43	2	no	—
276	#131	—	4	4	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	86	1	no	—
279	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
280	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	—	86	1	no	—
284	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
285	#127	C₄×D₄₃	1	1	yes	characteristic
286	#124	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	C₄×D₄₃	1	2	yes	—
289	C₄×Q₈	—	43	1	no	—
290	C₄×Q₈	—	43	1	no	—
291	C₄×Q₈	—	43	1	no	—
292	C₄×Q₈	—	43	1	no	—
293	C₄×Q₈	—	86	1	no	—
294	C₄×Q₈	—	86	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²×D₄₃	1	2	yes	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	86	1	no	—
299	C₂×C₄²	—	86	1	no	—
300	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
301	#106	—	43	2	no	—
302	#106	—	43	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	43	1	no	—
305	C₄⋊C₈	—	43	1	no	—
306	C₄⋊C₈	—	43	2	no	—
307	C₄⋊C₈	—	86	2	no	—
308	C₄⋊C₈	—	86	2	no	—
309	C₄⋊C₈	—	86	1	no	—
310	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
312	#103	—	43	2	no	—
313	#103	—	43	2	no	—
314	#102	—	43	2	no	—
315	#102	—	43	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	43	2	no	—
319	#97	—	86	2	no	—
320	#97	C₂²⋊D₄₃	1	2	yes	—
321	C₄×C₈	—	43	2	no	—
322	C₄×C₈	—	43	1	no	—
323	C₄×C₈	—	43	1	no	—
324	C₄×C₈	—	86	2	no	—
325	C₄×C₈	—	86	1	no	—
326	C₄×C₈	C₂²×D₄₃	1	2	yes	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	43	1	no	—
331	C₂×Q₈	—	43	1	no	—
332	C₂×Q₈	—	86	2	no	—
333	C₂×Q₈	—	86	1	no	—
334	C₂×Q₈	—	172	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	#10621898	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	SD₁₆	—	86	4	no	—
346	SD₁₆	—	172	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	4	no	—
349	M₁₆	—	172	2	no	—
350	M₁₆	#10621883	1	4	yes	complemented
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	—	43	2	no	—
356	C₂×C₈	—	43	2	no	—
357	C₂×C₈	—	86	1	no	—
358	C₂×C₈	—	86	2	no	—
359	C₂×C₈	—	86	1	no	—
360	C₂×C₈	—	172	2	no	—
361	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
362	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	43	1	no	—
365	C₄⋊C₄	—	43	1	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	1	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	86	1	no	—
375	C₄²	—	86	1	no	—
376	C₄²	—	86	1	no	—
377	C₄²	—	86	1	no	—
378	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
379	C₄²	#10621898	1	1	yes	characteristic
380	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
381	C₄²	C₂³×D₄₃	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
384	Q₈	—	4	2	no	—
385	Q₈	—	43	2	no	—
386	Q₈	—	86	1	no	—
387	Q₈	—	86	1	no	—
388	Q₈	—	86	1	no	—
389	Q₈	—	172	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	86	1	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	1	no	—
404	C₂×C₄	—	86	1	no	—
405	C₂×C₄	—	344	1	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#10621883	1	2	yes	—
411	C₂×C₄	#13063345	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	86	2	no	—
419	C₈	—	86	2	no	—
420	C₈	—	86	2	no	—
421	C₈	—	172	1	no	—
422	C₈	—	172	2	no	—
423	C₈	C₂×#10621883	1	4	yes	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₄×#10621883	1	2	yes	—
430	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	2	no	—
435	C₄	—	86	2	no	—
436	C₄	—	172	1	no	—
437	C₄	—	172	1	no	—
438	C₄	—	172	1	no	—
439	C₄	C₄×#10621883	1	2	yes	—
440	C₄	#131×D₄₃	1	1	yes	characteristic
441	C₄	#14583664	1	1	yes	characteristic
442	C₄	C₂²×#10621883	1	1	yes	characteristic
443	C₄	C₂×#13063345	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	#19143317	1	1	yes	characteristic
447	C₂	C₂×C₄×#10621883	1	1	yes	characteristic
448	C₂	#19143502	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2935	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₄₃×#532	C₂²
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2935	D₄₃
hypocenter	C₄₃	#17997
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. M₁₆×Dic₈₆	C₂	semidirect
3. #19133483	C₂	semidirect
4. #19133436	C₂	semidirect
5. #19133431	C₂	semidirect
6. C₈×#10621883	C₂	semidirect
7. #19133365	C₂	semidirect
9. C₂×#14582629	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
122. M₁₆×C₄₃	SD₁₆	semidirect
189. Dic₈₆	#131	semidirect
271. C₄₃	#17997	semidirect
350. M₁₆	#10621883	semidirect

Maximal subgroups

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

subgroup	index
#19144622	2
M₁₆×Dic₈₆	2
#19133483	2
#19133436	2
#19133431	2
C₈×#10621883	2
#19133365	2
#19133046	2
C₂×#14582629	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#2935	2
#17997	43