Subgroups — #25066571

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144644	C₂	1	1	yes	maximal, characteristic
2	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133461	C₂	1	2	yes	maximal, complemented
5	#19133454	C₂	1	2	yes	maximal, complemented
6	C₈×#10621873	C₂	1	2	yes	maximal, complemented
7	C₈×D₃₄₄	C₂	1	2	yes	maximal, complemented
8	#19133380	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133039	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133009	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₃	—	2	1	no	—
13	#14583433	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583235	C₄	1	1	yes	characteristic
16	#14583218	C₄	1	1	yes	characteristic
17	#14583200	C₄	1	2	yes	—
18	#14583115	C₄	1	2	yes	—
19	#14583052	C₄	1	1	yes	characteristic
20	#14583035	C₄	1	1	yes	characteristic
21	#14583029	C₂²	1	1	yes	characteristic, complemented
22	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
23	C₄×#10621873	C₂²	1	2	yes	—
24	C₄×D₃₄₄	C₂²	1	2	yes	—
25	#14582978	C₂²	1	1	yes	characteristic, complemented
26	#14582970	—	2	1	no	—
27	C₈×D₁₇₂	—	2	1	no	—
28	C₈×D₁₇₂	—	2	1	no	—
29	C₈×D₁₇₂	C₂²	1	2	yes	—
30	C₈×D₁₇₂	C₂²	1	2	yes	—
31	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
32	C₈×C₂²⋊D₄₃	—	2	1	no	—
33	#14582958	—	2	1	no	—
34	#14582956	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
37	#14582853	—	2	1	no	—
38	#14582652	C₂²	1	2	yes	complemented
39	#14582650	C₂²	1	2	yes	complemented
40	#14582631	C₂²	1	2	yes	complemented
41	#14582628	C₂²	1	2	yes	—
42	#14582628	C₂²	1	2	yes	—
43	#14582628	C₂²	1	2	yes	complemented
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#322	C₂²	1	2	yes	complemented
48	C₈²×C₄₃	C₂²	1	2	yes	complemented
49	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	—	2	1	no	—
51	C₂×#10621873	C₂×C₄	1	2	yes	—
52	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
53	C₂×#10621872	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₃	—	2	1	no	—
56	C₂×C₈×D₄₃	—	2	2	no	—
57	C₂×C₈×D₄₃	—	2	2	no	—
58	C₂×C₈×D₄₃	—	4	4	no	—
59	#13063319	—	2	1	no	—
60	#13063317	C₂×C₄	1	1	yes	characteristic
61	#13063313	C₂×C₄	1	1	yes	characteristic
62	#13063308	—	2	1	no	—
63	#13063304	C₂×C₄	1	1	yes	characteristic
64	#13063299	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
69	C₄×D₁₇₂	C₂³	1	2	yes	—
70	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
71	C₄×C₂²⋊D₄₃	—	2	1	no	—
72	#13063282	—	2	1	no	—
73	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
75	#13063259	C₂×C₄	1	2	yes	—
76	#13063257	C₂×C₄	1	2	yes	—
77	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
81	Dic₄₃⋊C₈	—	2	1	no	—
82	Dic₄₃⋊C₈	—	2	1	no	—
83	#13063250	C₂×C₄	1	2	yes	—
84	#13063247	C₂×C₄	1	2	yes	—
85	#13063247	C₂×C₄	1	2	yes	—
86	#13063247	C₂×C₄	1	2	yes	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
88	(C₂×D₄₃)⋊C₈	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	(C₂×D₄₃)⋊C₈	—	2	1	no	—
91	(C₂×D₄₃)⋊C₈	—	2	1	no	—
92	#13063236	—	2	1	no	—
93	#13063235	—	2	1	no	—
94	C₈×Dic₄₃	—	2	1	no	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
100	C₂²⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
102	#97×C₄₃	—	2	1	no	—
103	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₄₃	C₂³	1	2	yes	—
106	C₄×C₈×C₄₃	C₂³	1	2	yes	—
107	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂³×D₄₃	—	2	1	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	C₂×C₂²⋊D₄₃	—	2	1	no	—
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	—	2	4	no	—
117	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₄₃	—	2	2	no	—
120	C₂×C₄×D₄₃	—	2	1	no	—
121	C₂×C₄×D₄₃	—	2	2	no	—
122	C₂×C₄×D₄₃	—	4	2	no	—
123	C₂×C₄×D₄₃	—	4	2	no	—
124	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
125	M₁₆×C₄₃	—	2	4	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	4	1	no	—
129	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	#41	1	1	yes	characteristic
138	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₄₃	—	2	1	no	—
140	(C₂×D₄₃)⋊C₄	—	2	2	no	—
141	(C₂×D₄₃)⋊C₄	—	2	1	no	—
142	(C₂×D₄₃)⋊C₄	—	2	1	no	—
143	(C₂×D₄₃)⋊C₄	—	2	1	no	—
144	(C₂×D₄₃)⋊C₄	—	2	2	no	—
145	(C₂×D₄₃)⋊C₄	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
150	Dic₄₃⋊C₄	—	2	1	no	—
151	Dic₄₃⋊C₄	—	2	1	no	—
152	Dic₄₃⋊C₄	—	2	1	no	—
153	Dic₄₃⋊C₄	—	2	1	no	—
154	C₄×Dic₄₃	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	4	2	no	—
159	D₃₄₄	—	2	4	no	—
160	#10621873	—	2	4	no	—
161	#10621872	—	4	2	no	—
162	C₈×D₄₃	—	4	4	no	—
163	C₈×D₄₃	—	4	2	no	—
164	C₈×D₄₃	—	4	4	no	—
165	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₄₃	—	2	4	no	—
167	C₂²×D₄₃	—	2	2	no	—
168	C₂²×D₄₃	—	2	1	no	—
169	C₂²×D₄₃	—	4	2	no	—
170	C₂²×D₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₄₃	—	4	2	no	—
182	C₂×Dic₄₃	—	2	1	no	—
183	C₂×Dic₄₃	—	2	1	no	—
184	C₂×Dic₄₃	—	2	1	no	—
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	D₁₇₂	—	2	4	no	—
188	D₁₇₂	—	2	2	no	—
189	D₁₇₂	—	2	2	no	—
190	D₁₇₂	#131	1	4	yes	—
191	C₄×D₄₃	—	4	4	no	—
192	C₄×D₄₃	—	4	2	no	—
193	C₄×D₄₃	—	4	1	no	—
194	C₄×D₄₃	—	4	1	no	—
195	C₄×D₄₃	—	4	2	no	—
196	Dic₈₆	—	2	2	no	—
197	C₈×C₄₃	—	2	4	no	—
198	C₈×C₄₃	—	2	2	no	—
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	2	1	no	—
201	C₈×C₄₃	—	2	1	no	—
202	C₈×C₄₃	—	2	1	no	—
203	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₄₃⋊C₈	—	4	2	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	C₄₃⋊C₈	—	4	1	no	—
207	#17910	—	43	1	no	maximal, Sylow
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	#443	1	2	yes	—
211	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂×D₄₃	—	2	4	no	—
213	C₂×D₄₃	—	4	8	no	—
214	C₂×D₄₃	—	4	2	no	—
215	C₂×D₄₃	—	4	2	no	—
216	C₂×D₄₃	—	4	1	no	—
217	C₂×D₄₃	—	4	1	no	—
218	C₂×D₄₃	—	4	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	1	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	C₂×#131	1	2	yes	—
224	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₄₃	#575	1	1	yes	characteristic
226	Dic₄₃	—	4	1	no	—
227	Dic₄₃	—	4	2	no	—
228	Dic₄₃	—	4	1	no	—
229	Dic₄₃	—	4	1	no	—
230	#3105	—	43	1	no	—
231	#2966	—	43	1	no	—
232	C₂×C₈×D₄	—	43	1	no	—
233	#1586	—	43	2	no	—
234	#1585	—	43	2	no	—
235	C₈×SD₁₆	—	43	2	no	—
236	C₈×D₈	—	43	2	no	—
237	#1573	—	43	1	no	—
238	#1490	—	43	1	no	—
239	#1483	—	43	1	no	—
240	C₈×M₁₆	D₄₃	1	1	yes	characteristic, complemented
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	#2929	1	1	yes	characteristic
243	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
245	D₄₃	—	4	4	no	—
246	D₄₃	—	8	1	no	—
247	C₂³×C₈	—	86	1	no	—
248	#529	—	43	1	no	—
249	C₂×C₄×D₄	—	43	1	no	—
250	#484	—	43	1	no	—
251	#481	—	43	1	no	—
252	#478	—	43	2	no	—
253	#463	—	43	2	no	—
254	#450	—	43	1	no	—
255	#447	—	43	1	no	—
256	#446	—	43	1	no	—
257	C₈×Q₈	—	43	1	no	—
258	C₄×SD₁₆	—	43	2	no	—
259	C₄×D₈	—	43	2	no	—
260	#436	—	43	1	no	—
261	#435	—	86	1	no	—
262	C₈×D₄	—	43	1	no	—
263	C₈×D₄	—	43	2	no	—
264	C₈×D₄	—	43	2	no	—
265	C₈×D₄	—	86	1	no	—
266	C₈×D₄	—	86	1	no	—
267	C₈×D₄	—	86	1	no	—
268	#433	—	86	1	no	—
269	#432	—	43	1	no	—
270	#431	C₂×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	—	43	1	no	—
272	C₂×C₂²⋊C₈	—	86	1	no	—
273	#405	—	86	1	no	—
274	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
276	#335	—	43	2	no	—
277	#334	—	43	2	no	—
278	Q₈⋊C₈	—	43	2	no	—
279	D₄⋊C₈	—	43	2	no	—
280	D₄⋊C₈	—	43	2	no	—
281	D₄⋊C₈	—	43	2	no	—
282	#322	C₂×D₄₃	1	2	yes	complemented
283	C₈²	C₂×D₄₃	1	2	yes	complemented
284	C₄₃	#17910	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	—	43	1	no	—
286	C₂³×C₄	—	86	1	no	—
287	C₂×SD₁₆	—	43	2	no	—
288	C₂×D₈	—	43	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	86	1	no	—
291	C₂²×C₈	—	86	1	no	—
292	C₂²×C₈	—	86	2	no	—
293	C₂²×C₈	—	86	2	no	—
294	C₂²×C₈	—	86	1	no	—
295	C₂²×C₈	—	172	4	no	—
296	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
297	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
298	#126	—	86	1	no	—
299	#125	—	43	1	no	—
300	#124	—	43	1	no	—
301	#123	—	86	1	no	—
302	C₂²⋊Q₈	—	43	1	no	—
303	#121	—	43	1	no	—
304	C₄×Q₈	—	43	1	no	—
305	C₄×D₄	—	43	2	no	—
306	C₄×D₄	—	43	2	no	—
307	C₄×D₄	—	43	1	no	—
308	C₄×D₄	—	86	1	no	—
309	C₄×D₄	—	86	1	no	—
310	C₄×D₄	—	86	1	no	—
311	#117	—	86	1	no	—
312	C₂×C₄⋊C₄	—	43	1	no	—
313	C₂×C₂²⋊C₄	—	86	1	no	—
314	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
315	#107	—	43	2	no	—
316	#106	—	43	2	no	—
317	C₄⋊C₈	—	43	1	no	—
318	C₄⋊C₈	—	43	1	no	—
319	C₄⋊C₈	—	43	2	no	—
320	C₄⋊C₈	—	86	1	no	—
321	C₄⋊C₈	—	86	1	no	—
322	C₄⋊C₈	—	86	1	no	—
323	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
324	#103	—	43	2	no	—
325	#102	—	43	2	no	—
326	#102	—	43	2	no	—
327	#102	—	43	2	no	—
328	C₂²⋊C₈	—	86	1	no	—
329	C₂²⋊C₈	—	86	2	no	—
330	C₂²⋊C₈	—	86	2	no	—
331	C₂²⋊C₈	—	86	1	no	—
332	C₂²⋊C₈	—	86	1	no	—
333	C₂²⋊C₈	C₄×D₄₃	1	1	yes	characteristic
334	C₂²⋊C₈	C₄×D₄₃	1	1	yes	characteristic
335	#97	—	2	1	no	—
336	#97	—	86	1	no	—
337	#97	—	86	1	no	—
338	C₄×C₈	—	86	1	no	—
339	C₄×C₈	D₁₇₂	1	1	yes	characteristic
340	C₄×C₈	D₁₇₂	1	1	yes	characteristic
341	C₄×C₈	C₂²×D₄₃	1	2	yes	—
342	C₄×C₈	C₂²×D₄₃	1	2	yes	—
343	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
345	C₂⁴	—	86	1	no	—
346	C₂×Q₈	—	43	1	no	—
347	C₂×D₄	—	43	2	no	—
348	C₂×D₄	—	43	1	no	—
349	C₂×D₄	—	86	4	no	—
350	C₂×D₄	—	86	1	no	—
351	C₂×D₄	—	86	1	no	—
352	C₂²×C₄	—	86	1	no	—
353	C₂²×C₄	—	86	2	no	—
354	C₂²×C₄	—	86	1	no	—
355	C₂²×C₄	—	86	2	no	—
356	C₂²×C₄	—	172	2	no	—
357	C₂²×C₄	—	172	2	no	—
358	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
360	C₂²×C₄	#10621898	1	1	yes	characteristic
361	SD₁₆	—	86	4	no	—
362	D₈	—	86	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	172	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	86	1	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	2	no	—
371	C₂×C₈	—	172	4	no	—
372	C₂×C₈	—	172	2	no	—
373	C₂×C₈	—	172	4	no	—
374	C₂×C₈	—	172	2	no	—
375	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
376	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
377	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
378	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
379	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
380	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
381	C₄⋊C₄	—	43	1	no	—
382	C₄⋊C₄	—	43	1	no	—
383	C₄⋊C₄	—	43	2	no	—
384	C₄⋊C₄	—	86	1	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	1	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₂²⋊C₄	—	86	1	no	—
390	C₂²⋊C₄	—	86	2	no	—
391	C₂²⋊C₄	—	86	1	no	—
392	C₂²⋊C₄	—	86	1	no	—
393	C₂²⋊C₄	—	86	1	no	—
394	C₂²⋊C₄	—	86	2	no	—
395	C₂²⋊C₄	—	86	1	no	—
396	C₄²	—	86	1	no	—
397	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
398	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
399	C₄²	#10621898	1	1	yes	characteristic
400	C₄²	C₂³×D₄₃	1	1	yes	characteristic
401	C₂³	—	86	4	no	—
402	C₂³	—	86	2	no	—
403	C₂³	—	86	1	no	—
404	C₂³	—	172	2	no	—
405	C₂³	—	172	2	no	—
406	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
407	Q₈	—	86	2	no	—
408	D₄	—	43	4	no	—
409	D₄	—	86	4	no	—
410	D₄	—	86	2	no	—
411	D₄	—	86	2	no	—
412	D₄	—	172	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	1	no	—
419	C₂×C₄	—	86	1	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	172	4	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	—	172	2	no	—
424	C₂×C₄	—	172	1	no	—
425	C₂×C₄	—	172	1	no	—
426	C₂×C₄	—	172	2	no	—
427	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
428	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
429	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
432	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	172	2	no	—
440	C₈	—	172	1	no	—
441	C₈	—	172	1	no	—
442	C₈	#13063353	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	86	4	no	—
446	C₂²	—	172	8	no	—
447	C₂²	—	172	1	no	—
448	C₂²	—	172	1	no	—
449	C₂²	—	172	1	no	—
450	C₂²	—	172	2	no	—
451	C₂²	—	172	2	no	—
452	C₂²	#14583017	1	2	yes	—
453	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	172	1	no	—
459	C₄	—	172	1	no	—
460	C₄	—	172	2	no	—
461	C₄	—	172	1	no	—
462	C₄	#131×D₄₃	1	2	yes	—
463	C₄	C₂×#13063353	1	1	yes	characteristic
464	C₄	#14583699	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	344	1	no	—
467	C₂	—	172	4	no	—
468	C₂	#19143291	1	1	yes	characteristic
469	C₂	C₄×#13063353	1	1	yes	characteristic
470	C₂	C₂×#14583017	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#14583035	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₈×M₁₆	D₄₃
hypocenter	C₄₃	#17910
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #19143570	C₂	semidirect
3. C₂×C₈×D₁₇₂	C₂	semidirect
4. #19133461	C₂	semidirect
5. #19133454	C₂	semidirect
6. C₈×#10621873	C₂	semidirect
7. C₈×D₃₄₄	C₂	semidirect
8. #19133380	C₂	semidirect
9. #19133039	C₂	semidirect
10. #19133009	C₂	semidirect
11. C₈×M₁₆×C₄₃	C₂	semidirect
21. #14583029	C₂²	semidirect
22. C₈×Dic₈₆	C₂²	semidirect
25. #14582978	C₂²	semidirect
31. C₈×D₁₇₂	C₂²	semidirect
38. #14582652	C₂²	semidirect
39. #14582650	C₂²	semidirect
40. #14582631	C₂²	semidirect
43. #14582628	C₂²	semidirect
47. C₄₃×#322	C₂²	semidirect
48. C₈²×C₄₃	C₂²	semidirect
240. C₈×M₁₆	D₄₃	semidirect
282. #322	C₂×D₄₃	semidirect
283. C₈²	C₂×D₄₃	semidirect
284. C₄₃	#17910	semidirect

Maximal subgroups

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

subgroup	index
#19144644	2
#19143570	2
C₂×C₈×D₁₇₂	2
#19133461	2
#19133454	2
C₈×#10621873	2
C₈×D₃₄₄	2
#19133380	2
#19133039	2
#19133009	2
C₈×M₁₆×C₄₃	2
#17910	43